Video Analysis and Chronophotography in Physics: A Guide

How do you measure motion from a video? A video is not just an illustration: as soon as you know a reference length in the image and the time interval between two frames, it becomes a measuring instrument. This guide explains how that transformation works, what is actually measured, what is calculated, and under what conditions the result can be trusted. It covers both video analysis and chronophotography, on FizziQ Mobile and on FizziQ Web.

By Christophe Chazot, creator of FizziQ, an engineering graduate of École Polytechnique and a volunteer with the La main à la pâte Foundation. Last updated: 28 July 2026.

Introduction: how does a video become a measurement?

Film a falling ball, then measure its acceleration from the video. Depending on the method you use, you will get 9.8 m·s⁻² to within a few percent — or an unreadable scatter of points ranging from −5 to +20 m·s⁻². From exactly the same video, and exactly the same point marking.

That gap is not a flaw in the app, nor a lack of care on the student’s part. It follows from a fundamental property of the method, which runs through this entire guide:

Video analysis measures one quantity and one only: position. Velocity, acceleration, and energy are not measured — they are calculated from positions, and that calculation amplifies marking errors.

Understanding this is understanding why the position curve is always clean and the acceleration curve always noisy, why filming faster does not always give a better result, and why you never read the value of g off an acceleration curve.

A video becomes scientific data through a well-defined chain:

real motion → successive frames → spatial and temporal calibration → positions → velocities → accelerations → graphs → physical interpretation.

Every link in this chain brings its own assumptions and its own sources of error. This guide walks through them in order.

The quantities available at the end of the chain are the trajectory, the positions x(t) and y(t), displacement, velocity, acceleration, rotation angle and angular velocity, and — subject to explicit assumptions — kinetic, potential, and mechanical energy.

This is a guide to the method. For detailed operation of the app, two companion user manuals exist: the one for the Kinematics tool of FizziQ on smartphone and tablet, and the one for video analysis in FizziQ Web.

In brief — performing a kinematic analysis

Choose a video or a chronophotograph.

Place a known length in the plane of the motion.

Check the frame rate or the time interval.

Always mark the same point of the object.

Look at the positions first, then the velocities and accelerations.

To measure a constant acceleration, fit a model to the positions rather than reading the acceleration curve directly.

Introduction: how does a video become a measurement?
Part 1: what is image-based kinematic analysis?
Part 2: video or chronophotography?
Part 3: how an image becomes a measurement
Part 4: from position to velocity and acceleration
Part 5: shooting a usable video
Part 6: two FizziQ tools, mobile and desktop
Part 7: performing a kinematic analysis with FizziQ
Part 8: reading the graphs
Part 9: precision, uncertainties, and limits
Twelve experiments using video and chronophotography
Part 10: FizziQ compared with other software
Common errors and misconceptions
Frequently asked questions
Conclusion
Sources and references

Part 1: what is image-based kinematic analysis?

1.1 Kinematics and dynamics

Kinematics describes motion without concerning itself with causes: it answers the questions “where?”, “how fast?”, “with what acceleration?”. Dynamics deals with causes — forces and interactions — and connects the two through Newton’s laws.

Image-based analysis is a strictly kinematic method: it yields positions, and hence trajectories, velocities, and accelerations. It measures no forces. It is then the student who, through dynamical reasoning, interprets the measured acceleration as the signature of a force — for instance when concluding, from a constant vertical acceleration of 9.8 m·s⁻², that weight is the only significant force at work.

1.2 The system under study and the representative point

Before marking any points, you have to define the system: which object is being studied? Then choose the representative point that will be tracked frame after frame.

The underlying model is the point mass: the object is treated as a single point carrying all of its mass. This approximation is legitimate as long as the object’s dimensions are small compared with the distances travelled, and as long as its own rotation plays no part in what you are trying to study.

The ideal representative point is the centre of mass: it is the centre of mass that follows the parabolic trajectory of a projectile, even if the object is spinning. In practice, you mark a clearly identifiable visual feature (the apparent centre of a ball, a coloured marker, a joint). What matters most is to always mark the same feature: switching reference feature partway through introduces a systematic offset that shows up as a spurious jump in velocity.

For an extended, rotating object — a thrown hammer, a racket, an athlete — the centre of mass does not coincide with any visible point, and the discrepancy should be discussed explicitly rather than quietly ignored.

1.3 Frame of reference and coordinate system

A frame of reference is the object relative to which motion is described. In video analysis, it is the camera’s frame. As long as the camera is stationary with respect to the ground, this frame coincides with the Earth frame, which can be treated as inertial at the scale of a school experiment. If the camera moves, that assumption collapses and the measured positions mix the motion of the object with the motion of the operator: this is the first reason to keep the device still.

A coordinate system is the set of axes laid over that frame: an origin, an x-axis, a y-axis. Unlike the frame of reference, it is purely conventional, and FizziQ lets you place it wherever you like and reverse the direction of the axes. A sensible choice makes the analysis much easier: put the origin at the release point for a fall, point the y-axis upward so that gravitational acceleration comes out negative, align the x-axis with the direction of motion for a straight-line trajectory.

1.4 Trajectory, x(t), and y(t): three different graphs

A very common confusion, worth clearing up straight away:

the trajectory is the set of successive positions occupied in the plane, the parametric curve (x(t), y(t)), with no indication of time along the path. It can only be written as y(x) when each x-value corresponds to a single y-value: true for a projectile with no horizontal reversal, but not for a circle, a loop, or a vertical trajectory. A projectile’s trajectory is a parabola;
the curve x(t) gives horizontal position as a function of time. For that same projectile, it is a straight line;
the curve y(t) gives vertical position as a function of time. It is also a parabola, but it is not the same parabola as the trajectory, and it does not mean the same thing.

A student who recognises “a parabola” on screen without knowing which of the three they are looking at cannot draw a correct conclusion. The habit to instil is to name both axes before interpreting anything.

1.5 An old method, a recent tool

Studying motion through images predates computing by more than a century. In the 1870s and 1880s, Eadweard Muybridge settled the controversy over the horse’s gallop with burst photography, and Étienne-Jules Marey developed chronophotography and his photographic gun to break down bird flight and human walking. In the twentieth century, Harold Edgerton perfected stroboscopic photography and Berenice Abbott put high-speed photography to work illustrating the laws of physics.

Teachers took up the method as early as the 1980s, using a VCR and a transparency taped to the screen — a sound approach, but limited by the image quality of the day. What has changed today is therefore not the principle but the access: every student has a camera capable of filming at a high frame rate and a point-marking tool in the same device.

Part 2: video or chronophotography?

2.1 Two media, one principle

Both methods rest on the same idea: record the successive positions of an object at instants separated by a known time interval. They differ in the medium.

A video is a sequence of frames separated by an interval Δt set by the capture frame rate. You step through it frame by frame and mark one position on each of the frames you keep.

A chronophotograph is a single image on which the successive positions of one object are superimposed, likewise separated by a constant interval Δt. Historically it is produced by repeated shutter openings or by stroboscopic lighting; today it can also be produced by digitally compositing frames extracted from a video.

The practical difference is decisive: a video’s time interval is contained in the file; a chronophotograph’s is not. A chronophotograph carries no temporal information: the interval must come from the accompanying document or from the experimental protocol. This is an excellent opportunity to get students thinking about the fact that time, in a measurement, is never “in the image”: it always comes from an external standard.

2.2 What each medium offers

Chronophotography has a pedagogical strength all its own: the spacing between two successive positions is proportional to the average velocity over the interval. A lower-secondary student can therefore read off accelerated motion (positions spreading further apart), decelerating motion (positions bunching up), or uniform motion (constant spacing) directly, with no calculation and no formula. The motion becomes visible before it becomes calculable.

Video, on the other hand, lets you freely choose which portion of the motion to study, step backwards, correct a marked point, and adjust how many points are analysed.

Need	Suitable medium
Follow the full unfolding of the motion	Video
See the successive positions at a glance	Chronophotograph
Introduce acceleration qualitatively in lower secondary	Chronophotograph
Mark many positions and correct them	Video
Study fast motion frame by frame	High-frame-rate video
Work from a static document in a textbook	Chronophotograph
Study long or multi-phase motion	Video
Work with no camera and no equipment	Chronophotograph from the library

Both media are supported by FizziQ Mobile and FizziQ Web, with the same calculated quantities. To go further into classroom use of the static medium, see the article on using chronophotography in physics lab sessions.

Part 3: how an image becomes a measurement

A raw image contains only pixels and a frame number. To extract a physical measurement from it, you need two independent calibrations: a spatial one and a temporal one. These are the only two pieces of external information the method requires — and the two main sources of systematic error.

3.1 Spatial calibration: from pixels to metres

You identify in the image an object whose real length L is known, and read off the length ℓ it occupies in pixels. The scale factor is:

k = L / ℓ

with L in metres, ℓ in pixels, and k in metres per pixel. Every distance subsequently measured in pixels is multiplied by k.

This operation rests on a condition that is rarely stated and yet decisive:

The calibration reference must lie in the plane of the motion, that is, at the same distance from the camera as the object being studied.

A ruler placed against the back wall, or a tape measure held in front of the scene, is seen from a different angle than the object: it appears too small or too large, and every length, velocity, and acceleration in the experiment is affected by a wrong multiplicative factor. The error is purely systematic: it shows up neither in the scatter of the points nor in the shape of the curves, and no amount of smoothing will correct it. It is the most frequent and the most invisible error in all of video analysis.

The best reference is therefore an object placed exactly where the moving object passes: a tape measure fixed along the trajectory, a board of known dimensions, or the object itself if its size is accurately known.

3.2 Temporal calibration: Δt = 1/f

For a video at frame rate f (in frames per second), the time interval between two consecutive frames is:

Δt = 1/f

with f in frames per second (fps) and Δt in seconds. This relation assumes a constant frame rate: it ceases to hold for variable-frame-rate videos, produced by some automatic recording modes.

Frame rate	Δt between frames	Displacement of an object at 5 m·s⁻¹	Displacement at 20 m·s⁻¹
25 fps	40.0 ms	20 cm	80 cm
30 fps	33.3 ms	17 cm	67 cm
50 fps	20.0 ms	10 cm	40 cm
60 fps	16.7 ms	8.3 cm	33 cm
120 fps	8.3 ms	4.2 cm	17 cm
240 fps	4.2 ms	2.1 cm	8.3 cm

This table gives the practical rule for choosing a frame rate: between two frames you keep, the object should move a distance clearly larger than the marking uncertainty, yet small enough for the motion to be well described. A football struck at 20 m·s⁻¹ covers 67 cm between two frames at 30 fps: the trajectory is described by only a handful of points, and you need a higher frame rate. A ball rolling at 0.3 m·s⁻¹ covers just one centimetre at the same rate: here you should keep only every fifth or tenth frame.

In FizziQ this choice is set through the interval between points, independently of the video’s frame rate: you can mark every second frame, every fifth, every tenth. Marking every single frame is neither necessary nor desirable.

3.3 Origin and axes

The third setting is conventional: where to put the origin, and which way to orient the axes. FizziQ lets you move the origin and reverse the direction of each axis.

Two useful conventions:

for a fall or a launch, point the y-axis upward: gravitational acceleration then comes out negative, consistent with the usual form y(t) = y₀ + v₀ᵧ t − ½ g t²;
place the origin at a physically meaningful instant (release, contact, passage through equilibrium) rather than in a corner of the image.

These choices change no physical conclusion, but they do change the signs displayed — and a misread sign is a classic source of faulty reasoning.

3.4 What is measured, what is calculated

This is the central distinction of the guide, and it deserves to be stated explicitly.

Quantity	Status	Origin
Position x, y	Measured	User’s marked point × scale factor
Time t	Measured (by calibration)	Frame number × Δt
Velocity Vx, Vy, V	Calculated	Numerical differentiation of positions
Acceleration Ax, Ay	Calculated	Numerical differentiation of velocities
Angle, angular velocity	Calculated	Geometry of successive positions
Kinetic energy Ec	Calculated + assumption	Requires mass, entered by the user
Potential energy Ep	Calculated + convention	Requires mass and a chosen origin
Mechanical energy Em	Calculated + assumptions	Sum of the previous two

Energies deserve special mention. FizziQ asks for the object’s mass: this is not a measurement taken from the video, it is data supplied by the experimenter, with its own uncertainty. Gravitational potential energy, meanwhile, only has a value relative to a conventional origin: only its variations carry physical meaning. Presenting a potential energy value as an absolute property of the object is a lasting conceptual error.

3.5 The slow-motion trap: the error you cannot see

This is the number-one failure in video-analysis lab sessions, and it deserves a section of its own.

Videos shot in slow motion call for particular vigilance. Depending on the phone, the camera app, and the export method, the frame rate declared by the file may correspond to the playback rate rather than to the effective capture rate: a recording shot at 120 or 240 fps may be presented as playing back at 30 fps, with time dilated. The real interval between two frames is then 1/240 s, while the file announces 1/30 s. Other cases exist — consistent timestamps preserved, slow motion applied only at playback, re-encoding at another rate — hence the need to check rather than assume.

If the software trusts the declared frame rate, it believes Δt is 33.3 ms when it is actually 4.2 ms, eight times too large. The consequences compound:

all velocities are 8 times too small (v = Δx/Δt);
all accelerations are 64 times too small (a ∝ 1/Δt²).

A free fall filmed in slow motion and wrongly calibrated therefore yields an acceleration of about 9.81/64 ≈ 0.15 m·s⁻² instead of 9.81 m·s⁻². The curves remain perfectly smooth and perfectly plausible: nothing on the graph signals the error.

The check to run once per setup. Film a simple free fall, analyse it, and verify that the acceleration you obtain is around 9.8 m·s⁻². If the result is 8 or 64 times too small — or too large — the frame rate being used is wrong. This five-minute test validates one device, one camera setting, and one import or export method — that is, a complete chain, not a phone model in general.

FizziQ detects the frame rate automatically from the file’s metadata when it is present, and asks for manual entry otherwise. The exact behaviour depends on the phone model, the operating system, and the camera app used for the recording: which is precisely why the free-fall check remains indispensable.

For a chronophotograph the situation is no different: since the frame rate is never in the image, it must always be entered, and a wrongly entered rate produces exactly the same kind of invisible error.

Part 4: from position to velocity and acceleration

4.1 Average velocity and instantaneous velocity

Average velocity between two instants is displacement divided by duration. It is directly accessible from two marked positions:

v⃗_avg = (r⃗₂ − r⃗₁)/(t₂ − t₁)

Instantaneous velocity is the limit of that average velocity as the duration tends to zero. No experimental measurement can reach that limit: all you have are positions at discrete instants. What video analysis calls “velocity” is therefore always an estimate of instantaneous velocity built from average velocities over short intervals.

This nuance is not a matter of vocabulary. It explains everything that follows.

4.2 Estimation by central differences

The simplest and most symmetric estimate uses the positions bracketing the instant in question:

v⃗ᵢ ≈ (r⃗ᵢ₊₁ − r⃗ᵢ₋₁)/(2Δt)

Acceleration is obtained directly from the positions through the central second difference:

a⃗ᵢ ≈ (r⃗ᵢ₊₁ − 2r⃗ᵢ + r⃗ᵢ₋₁)/Δt²

with r⃗ in metres, v⃗ in m·s⁻¹, a⃗ in m·s⁻², and Δt in seconds. These relations are vectorial and apply separately to each component. Estimating acceleration by differentiating the central velocity twice would spread the points 2Δt apart and change the coefficients; it is the second difference above that is consistent with the uncertainties given below.

These are approximations. They improve as Δt gets small compared with the characteristic time of the motion — but, as we are about to see, a smaller Δt sharply degrades the noise. Choosing Δt is therefore a trade-off, not a one-way optimisation.

4.3 Why is acceleration always noisier than position?

Suppose each marked point carries a random error with standard deviation σ. Propagating uncertainties through the formulas above gives:

σ_v = σ/(Δt√2) and σ_a = σ√6/Δt²

The orders of magnitude become very telling with a concrete example. Take a video framing 2 m across 1280 pixels, that is 1.6 mm per pixel, and a realistic marking error of 2 pixels, so σ ≈ 3.1 mm.

Frame rate	σ on position	σ on velocity	σ on acceleration
25 fps	3.1 mm	0.06 m·s⁻¹	4.8 m·s⁻²
30 fps	3.1 mm	0.07 m·s⁻¹	6.9 m·s⁻²
60 fps	3.1 mm	0.13 m·s⁻¹	27.6 m·s⁻²
240 fps	3.1 mm	0.53 m·s⁻¹	441 m·s⁻²

(Values obtained by raw central-difference differentiation, without smoothing. See 4.5 for the effect of smoothing.)

The result is striking. A position error of 3 millimetres, entirely negligible to the eye, becomes at 30 fps an acceleration error of nearly 7 m·s⁻² — the order of magnitude of g itself. This is why the raw acceleration curve of a free fall looks like a scatter of points centred, at best, on the right value.

Each differentiation divides by Δt and loses an order of quality: position is measured, velocity is acceptable, acceleration is fragile.

4.4 The high-frame-rate paradox

The table above contains a counterintuitive result that should be stated plainly:

At constant marking error, filming faster degrades the point-by-point calculated acceleration.

Going from 30 to 240 fps divides Δt by 8, hence Δt² by 64: the uncertainty on acceleration is multiplied by 64. A high frame rate is useful for describing fast motion in detail — that is, for having enough points and avoiding blur — but it does not automatically deliver a better acceleration.

The right way to exploit a high frame rate is to not mark every frame, or to compute the derivatives over an interval wider than the interval between frames. That is exactly what FizziQ’s interval-between-points setting allows. Filming at 240 fps and then marking every eighth frame is, from the noise point of view, equivalent to filming at 30 fps — while keeping the advantage of individually sharper frames.

4.5 What FizziQ does

FizziQ does not settle for raw differences: the kinematic analysis product page states that a 5-point moving smoothing is applied to the calculation of derived quantities, and FizziQ’s earlier guide mentions a local quadratic fit.

A 5-point moving quadratic fit reduces noise appreciably: in the numerical example considered, and under the same assumptions, it brings the acceleration uncertainty down from 6.9 to about 1.5 m·s⁻² at 30 fps. That is an improvement by a factor of roughly 4.5 in this case, and it explains why the curves FizziQ displays are far more readable than raw derivatives.

It changes nothing about the hierarchy, however: acceleration remains by far the most fragile quantity. And smoothing has a cost worth knowing: it attenuates rapid variations and rounds off discontinuities. On a bounce or a collision, 5-point smoothing spreads the event over five intervals and underestimates the peak. As a general rule:

A smoothed signal is more readable; it is not more accurate.

4.6 The right method: fit a model to the positions

From all of the above follows one major practical consequence, and it is what separates a good analysis from a rough one:

To measure a constant acceleration, do not use the acceleration curve. Fit a parabola to the positions.

For a free fall, the model y(t) = y₀ + v₀ᵧ t − ½ g t² is compared directly with the measured positions. The fit uses all the points at once, and each marking error compensates statistically instead of being amplified.

The performance gap is considerable. Under the same assumptions as before (σ = 3.1 mm, 30 fps) and a one-metre fall observed over about 14 frames:

acceleration read point by point off the curve: uncertainty of order 7 m·s⁻²;
g obtained by parabolic fit to the positions: uncertainty of order 0.10 m·s⁻².

That is a factor of roughly 70, from exactly the same data. It is the most useful message this guide can pass on to a teacher.

The same logic applies to other models: a linear regression on x(t) gives a far more reliable velocity than the average of point-by-point velocities; a sinusoidal fit to a pendulum’s position gives a far more reliable period than reading off maxima.

FizziQ supports this fitting in the experiment notebook, which offers modelling and interpolation options on graphs.

Key point. Point-by-point instantaneous acceleration is there to show the shape of a motion — whether the acceleration is constant, increasing, alternating. It is not there to measure its value. To measure, fit a model to the positions.

Part 5: shooting a usable video

Contrary to a widespread intuition, the hard part of video analysis is not the point marking: it is the filming. A badly shot video cannot be rescued by any later processing, whereas mediocre marking on a good video can always be corrected.

5.1 The ten rules

Keep the camera still. Tripod, mount, or device resting on a stable surface. A moving camera moves the frame of reference, and the measured positions then mix two motions.
Put the optical axis perpendicular to the plane of the motion, aimed at the middle of the trajectory. This is the condition that limits perspective errors.
Keep the motion in a single plane. The analysis returns two coordinates: any displacement towards the camera or towards the background is lost, and distorts apparent lengths.
Put the calibration reference in that same plane (see 3.1). Non-negotiable.
Choose a well-contrasted, clearly identifiable moving object. A brightly coloured sticker on the object beats a dark object against a dark background.
Light the scene well. A poorly lit sensor automatically lengthens the exposure time, which produces motion blur and makes marking uncertain by several pixels.
Choose the frame rate to match the speed (see the table in 3.2), and verify the frame rate actually used (see 3.5).
Avoid zooming and any camera movement during the shot. Zooming changes the scale factor mid-recording: the calibration is no longer valid.
Frame the whole trajectory, from the first to the last useful instant, allowing a margin.
Check the file before leaving the site of the experiment. An unusable video discovered in class the next day is a lost session.

These rules are covered in detail in the article on seven tips for shooting a good kinematics video.

5.2 Four optical defects worth knowing

Parallax. If the camera is not facing the middle of the trajectory, points far from the optical axis are seen obliquely and their apparent positions are shifted. The effect is zero at the centre and grows towards the edges: it distorts the trajectory non-uniformly, which is particularly insidious because it looks like a physical effect.

Perspective. An object moving away from the camera appears smaller and slower. For strictly planar motion perpendicular to the optical axis, the effect is absent; as soon as the motion has a component in depth, it appears. This is why a football shot filmed from the side can be analysed while the same shot filmed from the goal cannot.

Lens distortion. The wide-angle lenses of smartphones bend straight lines near the edges of the image. On a straight trajectory crossing the whole field, this can create an apparent curvature. The remedy is simple: step back and frame wider than necessary, so that the motion stays in the central zone.

Rolling shutter. Most smartphone CMOS sensors do not expose the whole image at the same instant: they scan it line by line. A fast horizontally moving object then appears slanted or distorted, and positions read at the top and bottom of the object do not correspond to the same instant. The effect stays modest for ordinary school-scale motion, but becomes visible on very fast objects (a propeller, a struck tennis ball). Its magnitude depends heavily on the phone model.

To these four defects add motion blur: if the object covers an appreciable distance during the exposure, its image is smeared and marking becomes ambiguous. Plentiful lighting, allowing a short exposure, is the best remedy.

5.3 Precautions

Read before any experiment. Protect the phone doing the filming as well as any phone being filmed (case, padding). Never throw a device. Keep drop experiments to modest heights, over a cushion or padded landing. Never place anyone in the path of a thrown object, and keep the landing area clear. Do not film while driving: in-vehicle experiments are carried out by a passenger. For sports activities, follow the usual rules of the practice and obtain the consent of those being filmed; publishing images of students falls under image rights and the institution’s own rules.

5.4 Filming is not always necessary

Not every session has to begin with a shoot. FizziQ includes a library of kinematics videos and a library of chronophotographs ready to be marked, accessible directly in the app. They let you devote the session to analysis rather than logistics, and guarantee that every student is working from a usable source. Their use is described in the article on the FizziQ video library.

An effective progression often consists of starting with a library video, to establish the method, and then having students shoot their own videos once they know what a good video needs to contain.

Part 6: two FizziQ tools, mobile and desktop

Kinematic analysis exists in two distinct FizziQ environments, which share the same measurement principles but not the same interface. They are complementary, not competing.

6.1 FizziQ on smartphone and tablet

The mobile app lets you film and analyse with the same device, which removes any file-transfer step. Its strengths:

capture and analysis in the same session, in class or in the field;
import of a video or chronophotograph from the gallery or from a web address;
access to the built-in library of videos and chronophotographs;
touch marking, correction, and deletion of points;
calculation of positions, velocities, accelerations, rotations, and energies;
transfer of data to the experiment notebook, then graphs, modelling, and export;
offline operation once the app is installed.

The complete sequence — choosing the source, checking the frame rate, calibrating, marking, results, notebook — is described step by step in the user manual for the Kinematics tool of FizziQ on smartphone and tablet.

6.2 FizziQ Web on a computer

FizziQ Web is an application that runs in the browser, with no installation, and offers the full kinematic analysis. Its strengths:

no installation, no account: the tool opens in a browser;
usable on the institution’s computers and Chromebooks, including where smartphones are unavailable or not permitted;
mouse marking, generally more comfortable and easier to control on a large screen;
a large screen, suited to projection and to two students working at one station;
import of videos and chronophotographs, access to the library;
calculation of positions, velocities, accelerations, rotations, and energies;
built-in scientific spreadsheet, graphs and interpolations, report writing and export.

The detail of the commands is given in the dedicated documentation on video analysis in FizziQ Web.

FizziQ Web is not a display layer for the mobile app: it is a distinct piece of software, with its own screens and its own interactions.

6.3 Which environment to choose?

Situation	FizziQ Mobile	FizziQ Web
Filming the experiment directly	Very well suited	Requires importing the video
Working in the field, away from the classroom	Very well suited	Poorly suited
Analysis on smartphone or tablet	Yes	No
Analysis on a computer or Chromebook	No	Yes
Marking by finger	Yes	No
Marking by mouse	No	Yes
Large screen and projection	Limited	Very well suited
Installation required	App to install	None, in the browser
Writing up a report on a keyboard	Limited	Very well suited
Spreadsheet and data processing on a large screen	More limited	Very well suited
Institution not permitting smartphones	Not workable	Recommended solution

The most effective arrangement is often to film with the mobile and analyse on the computer: the smartphone camera remains the best capture tool, the computer the best marking and writing tool.

Part 7: performing a kinematic analysis with FizziQ

FizziQ lets you study a motion from a video or a chronophotograph:

on a smartphone or tablet with the FizziQ app;
on a computer or Chromebook with FizziQ Web.

The procedure is the same in both environments: choose the medium to analyse, set the spatial scale and the time parameters, mark the object’s successive positions, then work with the calculated quantities.

On a smartphone or tablet, marking is done directly on the touchscreen. In FizziQ Web, it is done with the mouse or the trackpad.

7.1 Opening the kinematic analysis

In FizziQ on a smartphone or tablet:

tap the name of the instrument shown at the top of the screen;
select Kinematic Analysis;
choose Video kinematics or Chronophotography.

In FizziQ Web, open the Kinematics module, then choose Video analysis or Chronophotography.

In both cases, the experimental approach is identical.

7.2 Choosing a video or a chronophotograph

For a video analysis

You can use:

a video recorded with the smartphone or tablet;
a video stored on the computer;
a video from the FizziQ teaching library;
a video built into the app;
a video downloaded from a web address.

The FizziQ library offers sequences suited to kinematic analysis: free fall, projectile motion, pendulum, collisions, sports movements, vehicles or accelerated motion.

For a first hands-on session, it is best to use a library video. The motions are clearly visible and the filming conditions are suited to point marking.

For a chronophotograph

You can use:

an image stored on the device;
a chronophotograph from the FizziQ library;
a chronophotograph created from a video.

A chronophotograph gathers several successive positions of an object onto a single image. It lets you study the trajectory and the way the distances travelled change, directly.

7.3 Setting the scale and the coordinate system

Setting the spatial scale

Before marking the motion, you have to convert the distances measured in the image, expressed in pixels, into real distances expressed in metres.

Two markers appear on the image: an origin and an endpoint.

move the first marker to one end of the reference object;
place the second marker at its other end;
select Ruler length;
enter the real length of the object;
confirm.

For example, if a 1-metre ruler appears in the image, place the two markers on its ends and enter the value 1.

The object used for calibration must lie in the same plane as the motion under study. If it sits noticeably in front of or behind the moving object, the resulting scale will be wrong.

The camera should also be placed as perpendicular as possible to the plane of the motion, to limit perspective distortion.

Choosing the origin and axes

The origin of the coordinate system can be placed at a point that is meaningful for the experiment:

at the object’s starting point;
at the release point of a dropped object;
at ground level;
at the centre of a circular motion;
at the equilibrium point of a pendulum.

In the advanced settings, the Detach origin option lets you place the point (0, 0) independently of the ruler used for calibration.

You also have to choose the orientation of the axes.

For a free fall or a projectile motion, it is often convenient to orient:

the x-axis horizontally to the right;
the y-axis vertically upward.

With this convention, the acceleration of gravity is negative on the vertical axis.

The choice of origin and axis orientation does not change the observed motion. It only changes the coordinates and their signs.

7.4 Checking the time parameters

Analysing a motion requires knowing the time interval between two successive positions. The setting depends on the medium used.

For a video analysis

The video’s frame rate is shown at the bottom right of the screen. It is the number of frames recorded each second and is expressed in frames per second, or fps.

FizziQ usually recognises this frame rate automatically. It is nonetheless necessary to check it, especially when the video:

was recorded in slow motion;
was downloaded from the internet;
was converted or re-compressed;
does not contain reliable metadata.

The advanced settings, reached from the Tools button or the settings button, let you change several items.

Setting	Function
Frame rate	Change the number of frames per second if the detected value is not correct
Sampling	Mark only every second, third or later frame
Detach origin	Place the origin independently of the calibration ruler
Rotation	Change the orientation of the image

Sampling does not change the video’s frame rate. It sets the number of frames between two marked points.

For example, with a video recorded at 30 frames per second:

if every frame is marked, the time interval is 1/30 s;
if one frame in three is marked, the time interval is 3/30 s, that is 0.10 s.

It is not always useful to mark every frame. For a slow motion or a video recorded at a high frame rate, a larger sampling gives sufficiently spaced positions and reduces the relative effect of marking imprecision.

For a chronophotograph

The time interval between two positions can be checked and changed directly at the time of marking.

This value must match the real duration between two successive frames used to create the chronophotograph.

If the chronophotograph comes from a video, the time interval depends on the video’s frame rate and the number of frames between two retained positions:

Δt = N / f

where N is the number of frames between two positions and f the video’s frame rate in frames per second.

For example, if one position is kept every four frames in a video at 40 frames per second:

Δt = 4/40 = 0.10 s

If the time interval is unknown, you can still study the trajectory and the relative spacing of the positions. The calculated velocity and acceleration values, however, cannot be treated as quantitatively reliable.

7.5 Marking the motion

Marking consists in locating the position of the same point of the object at different instants.

choose a precise, easily identifiable point on the object;
bring the target onto this point;
tap the screen or click with the mouse to record the position;
move to the next frame;
place the target back on the same point;
repeat until the end of the sequence under study.

The chosen point can be:

the apparent centre of a ball;
a coloured sticker;
a point marked on an object;
a specific joint in the study of a sports movement;
the centre of a moving object.

It is essential to always mark the same point. Switching from the centre of an object to its edge during the analysis would introduce an artificial error in the positions, then in the calculated velocities and accelerations.

In a video, FizziQ automatically advances to the next frame, taking the selected sampling into account.

In a chronophotograph, the user marks the various positions visible on the image in turn, in chronological order.

Several controls make marking easier:

Control	Function
Navigation arrows	Move forward or back through the video
Eye	Hide or show the points already placed
Bin	Delete the markers
Photo	Create an image of the trajectory
Result	Access the calculated quantities

If you make a mistake, it is better to go back immediately to the position concerned and correct the point before continuing the analysis.

7.6 Examining the results

Once marking is finished, select Result.

FizziQ automatically computes the main kinematic quantities.

Category	Quantities	Unit
Position	x, y	m
Velocity	Vx, Vy, V	m·s⁻¹
Acceleration	Ax, Ay, A	m·s⁻²
Rotation	angle α	degrees
Energy	Ec, Ep, Em	J

Energies can be calculated once the object’s mass and the necessary parameters have been entered.

It is advisable to examine the results in the following order:

check the trajectory and the positions;
study the velocity components;
then examine the accelerations;
compare the results with the expected physical model.

Velocities are calculated from the positions. Accelerations are themselves calculated from the velocities. Each differentiation amplifies the small marking imprecisions.

An irregular acceleration curve therefore does not necessarily mean that the motion is irregular. It may simply reflect the marking uncertainties.

7.7 Working with the data in the experiment notebook

The selected quantities can be transferred to FizziQ’s experiment notebook.

It then becomes possible to:

view the values in a table;
plot the quantities against time;
compare several curves;
carry out a mathematical model fit;
add observations and conclusions;
export or share the report.

To obtain a reliable measurement, it is generally better to fit a model to the whole set of positions than to read a single isolated value of velocity or acceleration.

A few examples:

for uniform straight-line motion, fit a straight line to x(t);
for a free fall, fit a parabola to y(t);
for a pendulum, fit a sinusoidal function to the position;
for uniform circular motion, study how the angle or the coordinates x(t) and y(t) change.

In the case of a free fall, the model can be written:

y(t) = y₀ + v₀ᵧ t + ½ a_y t²

The coefficient of the t² term gives the vertical acceleration. If the vertical axis points upward, you should obtain a value close to:

a_y ≈ −9.8 m·s⁻²

7.8 Creating a chronophotograph from a video

FizziQ can also turn a video into a chronophotograph.

In FizziQ Mobile, open the Tools tab, then select Video Chrono. The same function is available in FizziQ Web.

Three main parameters must be set:

Parameter	Role
Frame rate	Give the video’s number of frames per second
Interval	Keep one frame in N, from 1 to 10
Sensitivity	Adjust motion detection relative to the background

For a readable chronophotograph:

use a fixed camera;
film a motion in a well-defined plane;
choose a still background;
create enough contrast between the moving object and the background;
avoid moving shadows;
set the interval so that the successive positions do not overlap too much.

The time interval between two positions of the chronophotograph depends on the video’s frame rate and the interval chosen during conversion. This information must be kept for the quantitative analysis.

7.9 Tips for a successful analysis

The quality of the results depends first of all on the quality of the filming.

Stabilise the camera

Use a tripod or place the device on a stable support. A movement of the camera during recording would be interpreted as a movement of the object.

Film perpendicular to the motion

The camera’s axis must be as perpendicular as possible to the plane in which the object moves. This reduces perspective errors.

Place a reference object in the plane of the motion

The ruler or object of known length must be at the same distance from the camera as the moving object under study.

Use a contrasting background

The tracked point must be clearly visible on every frame. A coloured sticker can make marking easier.

Light the scene properly

Insufficient lighting produces blur and makes the object’s position hard to determine. It is better to use bright, even lighting.

Avoid motions that are too fast or too small

The object must occupy a sufficient size in the image and move a measurable distance between two frames. A higher frame rate may be needed for fast motions.

Limit the length of the sequence

It is generally not necessary to analyse the whole video. Selecting only the useful part of the motion reduces the marking time and makes interpretation easier.

7.10 A recommended first exercise: studying a free fall

To get to know the tool, use a free-fall video available in the FizziQ library.

open the kinematic analysis;
select Video kinematics;
choose a free-fall video;
set the scale using the reference object;
check the frame rate shown at the bottom right;
orient the vertical axis upward;
mark the centre of the ball on each useful frame;
display the vertical position y against time;
transfer the data to the notebook;
fit a parabola to y(t).

The model obtained should be close to:

y(t) = y₀ + v₀ᵧ t − ½ g t²

The value of g deduced from the fit should be close to 9.8 m·s⁻².

This first activity gives an understanding of the whole approach: calibration, marking, calculation of the quantities, graphical representation and comparison with a physical model.

7.11 FizziQ Mobile or FizziQ Web: which to choose?

The analysis method is identical in both environments.

FizziQ Mobile is particularly suited to:

filming and analysing with the same device;
working in the field;
using a tablet in class;
running an experiment quickly.

FizziQ Web is particularly suited to:

working on a computer or Chromebook;
marking with the mouse on a large screen;
projecting the analysis in front of the class;
writing the report on a keyboard;
using FizziQ in a digital environment such as Capytale.

The two tools are complementary. A video can be recorded with a smartphone or tablet, then analysed on a computer with FizziQ Web.

Part 8: reading the graphs

A graph only speaks if you know what the motion you are looking for should look like. Here are the signatures of the most commonly studied motions. Throughout what follows, the y-axis points upward and air resistance is neglected unless stated otherwise.

8.1 Uniform straight-line motion

x(t): a straight line;
v(t): constant, up to marking fluctuations;
a(t): a scatter centred on zero.

This is the best motion for showing students the noise of differentiation: position is clean, velocity acceptable, acceleration unreadable — even though we know by construction that it is zero. The experiment is as much a lesson in metrology as in kinematics.

8.2 Uniformly accelerated straight-line motion

x(t): a parabola;
v(t): a straight line whose slope is the acceleration;
a(t): constant, very noisy.

The right way to measure the acceleration is the slope of v(t), or better still the quadratic coefficient of a parabolic fit to x(t) — never the average of the a(t) curve.

8.3 Free fall

Model, with the y-axis pointing up:

y(t) = y₀ + v₀ᵧ t − ½ g t²

with y in metres, t in seconds, v₀ᵧ in m·s⁻¹, and g ≈ 9.81 m·s⁻². Fitting this parabola to the positions gives g with good precision (see 4.6). A one-metre fall lasts about 0.45 s, that is roughly fifteen frames at 30 fps: not many, so framing a sufficient drop height is essential.

8.4 Projectile motion

horizontally: x(t) linear, Vx essentially constant;
vertically: y(t) parabolic, Vy linearly decreasing;
trajectory y(x): a parabola.

This is the canonical experiment on the decomposition of motion: the two components are independent, and students see that the horizontal motion ignores gravity. A noticeable departure from constant Vx signals air resistance, which also makes this a good entry point into the limits of the model.

8.5 Uniform circular motion

trajectory: a circle;
speed (magnitude of velocity): constant;
direction of the velocity vector: rotating;
acceleration: directed towards the centre, of magnitude v²/R.

This motion is the counterexample that breaks the misconception “constant speed, therefore zero acceleration”. Video analysis makes it visible by plotting the successive velocity vectors: their magnitude does not change, their direction changes continuously.

8.6 Pendulum

position: a periodic signal of period T;
velocity: maximum when passing through equilibrium, zero at the extremes;
energy: exchange between Ep and Ec, with Em approximately constant if dissipation is weak.

For the small oscillations of a simple pendulum, T = 2π√(L/g), that is about 1.42 s for L = 0.5 m and 2.01 s for L = 1.0 m. The period is measured far more reliably by timing ten oscillations on the position curve than by locating two consecutive maxima.

8.7 Bounces

y(t): a succession of parabolic arches of decreasing amplitude;
velocity: a sign discontinuity at each impact;
mechanical energy: a stepwise decrease, one step per bounce.

Beware of smoothing on this motion: the impact is a discontinuity, and 5-point smoothing spreads it artificially (see 4.5). Each arch should be analysed separately rather than the whole motion in one go.

Part 9: precision, uncertainties, and limits

9.1 The uncertainty budget of a video analysis

A video analysis accumulates errors of two very different natures, and learning to tell them apart matters.

Random errors vary from point to point and show up in the scatter:

marking uncertainty, typically 1 to 3 pixels depending on contrast, the apparent size of the object, and sharpness;
motion blur, which widens the target;
image resolution, which sets the floor.

Systematic errors shift every point in the same direction and show up on no graph at all:

a calibration reference outside the plane of the motion (wrong scale factor);
a wrong frame rate, especially in slow motion (wrong time scale);
parallax and perspective (geometric distortion);
a change of reference feature partway through marking (abrupt offset);
lens distortion.

This distinction is pedagogically decisive: students spontaneously try to reduce scatter by marking more carefully, whereas the most consequential errors are invisible in the scatter. To go further, see the guide to understanding measurement uncertainty with a smartphone.

9.2 No, adding points does not always improve precision

A stubborn piece of received wisdom needs correcting here, one that still appears in some documentation, including an older FizziQ user manual:

“The more points you add, the more precise the analysis” is false in general.

What is true: increasing the number of points over a given duration, and then fitting a model to the whole set, does improve the result, because the fit averages more independent measurements.

What is false: reducing the interval Δt between consecutive points does not improve point-by-point velocities and accelerations — it degrades them, as section 4.3 shows. At equal marking error, halving Δt doubles the uncertainty on velocity and quadruples it on acceleration.

The useful rule is therefore: choose Δt large enough that the displacement between two points far exceeds the marking uncertainty, and small enough to describe the variations of the motion properly. A motion described by 15 to 30 well-chosen points beats a motion described by 200 points crammed together.

9.3 The limits of the model

Beyond measurement uncertainty, some conclusions are limited by the assumptions of the model rather than by data quality:

the point mass: the object is reduced to a point, its rotation and extension ignored;
planar motion: the third dimension is lost;
the mass entered for energies: external data, with its own uncertainty;
the origin of potential energy: a convention, on which every displayed value of Ep and Em depends;
neglected friction: an often implicit assumption, and one that video analysis is well placed to test.

A good student conclusion always distinguishes “the measurement is imprecise” from “the model does not apply”. These are two different diagnoses calling for two different remedies.

Twelve experiments using video and chronophotography

The experiments below are ordered by increasing difficulty. The precautions in section 5.3 apply to all of them. The full catalogue is available in the FizziQ activities.

School levels are given for the French system with approximate international equivalents: cycle 4 ≈ lower secondary, ages 12–15; seconde ≈ grade 10, ages 15–16; première ≈ grade 11, ages 16–17; terminale ≈ grade 12, ages 17–18.

Experiment 1: reading a motion from a chronophotograph, without calculation

Scientific question: how do you recognise accelerated, decelerating, or uniform motion by eye?
Level: lower secondary, grade 10.
Duration: 20 min.
Medium: chronophotograph (FizziQ library or a textbook document).
Equipment: a device running FizziQ, or a simple projection.
Procedure: observe the spacing between successive positions, describe it, then sort several chronophotographs by type of motion.
Quantities: no numerical measurement at this stage; relative distances.
Representation: the annotated image itself.
Model: at constant time interval, spacing is proportional to average velocity.
Expected result: correct classification of the motions with no calculation at all.
Source of uncertainty: visual perception of small differences.
Interpretation: the motion becomes visible before it becomes calculable.
Permitted conclusion: this motion is speeding up / slowing down / uniform.
Conclusion not permitted: a numerical value of velocity or acceleration.

Experiment 2: uniform straight-line motion and differentiation noise

Question: what are the velocity and acceleration of an object moving steadily?
Level: grade 10.
Duration: 45 min.
Medium: video (self-propelled cart, trolley, person walking, rolling ball).
Procedure: film perpendicular to the motion with a calibration reference in the plane; mark about twenty positions; display x(t), V, and A in turn.
Quantities: position, velocity, acceleration.
Representation: x(t), V(t), A(t).
Model: x(t) = x₀ + v t.
Expected result: x(t) straight, V roughly constant, A unreadable around zero.
Difficulties: regularity of the motion, calibration reference in the plane.
Interpretation: the real acceleration is zero; the scatter observed measures marking noise, not a physical phenomenon.
Conclusion not permitted: “the acceleration varies”.
Resource: the Uniform straight-line motion activity.

Experiment 3: measuring g by parabolic fit

Question: what value of gravitational acceleration does video analysis give?
Level: grades 10–11.
Duration: 1 h.
Medium: video of a fall (library, or a ball dropped in front of a tape measure).
Procedure: calibrate on the tape measure placed in the plane of the fall; mark every position of the fall; plot y(t); fit a parabola in the experiment notebook; deduce g. Compare with the value read off the acceleration curve.
Quantities: y(t), quadratic coefficient, g.
Representation: y(t) with the model curve superimposed.
Model: y(t) = y₀ + v₀ᵧ t − ½ g t².
Expected result: g within a few percent of 9.8 m·s⁻² by fitting; a widely scattered value by direct reading of A.
Difficulties: short fall duration (≈ 0.45 s for 1 m), motion blur, the file’s actual frame rate.
Interpretation: the gap between the two methods illustrates the amplification of noise by differentiation.
Resources: the Measuring g by kinematic analysis and Galileo: free fall activities.

Experiment 4: decomposing projectile motion

Question: are the horizontal and vertical motions independent?
Level: grade 11.
Duration: 1 h.
Medium: video of a ball or thrown object, filmed from the side.
Procedure: mark the whole trajectory; display x(t), y(t), Vx, and Vy separately.
Quantities: x, y, Vx, Vy.
Representation: the trajectory y(x), then the four time curves.
Model: Vx constant, Vy linearly decreasing, y(t) parabolic.
Expected result: Vx appreciably constant, Vy decreasing with a slope close to −g.
Difficulties: genuinely planar motion, ball moving away from the camera.
Interpretation: gravity acts only on the vertical component.
Permitted conclusion: within the uncertainty, Vx is constant — so friction is negligible at this scale.
Resources: the Basketball and Football: penalty kick activities.

Experiment 5: quantifying friction

Question: under what conditions does the “negligible friction” model stop being valid?
Level: grades 11–12.
Duration: 1 h 30.
Medium: video of two very different objects (a badminton shuttlecock and a tennis ball, or a bead falling in water and in air).
Procedure: analyse both motions under the same conditions; compare Vx against time, or the departure of y(t) from the model parabola.
Quantities: position, velocity, departure from the model.
Representation: data superimposed on the frictionless model.
Expected result: agreement for the dense, compact object; a growing departure for the light, bulky one.
Difficulties: making the two shots comparable.
Interpretation: here the departure from the model is physical information, not measurement error — hence the importance of having first characterised the marking noise (Experiment 2).

Experiment 6: energy dissipation during bounces

Question: what fraction of the mechanical energy is lost at each bounce?
Level: grade 11.
Duration: 1 h.
Medium: video of a ball bouncing in front of a vertical scale.
Procedure: mark several successive arches; read the maximum height of each bounce; compute the ratio of two successive heights.
Quantities: maximum heights, potential energy at the apex.
Representation: full y(t), then maximum height against bounce number.
Model: at the apex, the energy is entirely potential; the ratio of heights gives the ratio of energies.
Expected result: an approximately geometric decrease in the heights.
Difficulties: smoothing rounds off the impacts; analyse arch by arch.
Interpretation: the loss occurs at contact, not during flight.
Conclusion not permitted: attributing the loss to air resistance without testing it separately.

Experiment 7: pendulum, period, and energy exchange

Question: how is energy distributed over an oscillation?
Level: grades 11–12.
Duration: 1 h 30.
Medium: video of a pendulum filmed head-on, with the string length measured.
Procedure: mark several oscillations; enter the mass; display Ec, Ep, and Em; measure the period over ten oscillations.
Quantities: position, velocity, Ec, Ep, Em, period.
Representation: the three energies superimposed against time.
Model: T = 2π√(L/g) for small amplitudes.
Expected result: Ec and Ep in antiphase, Em approximately constant; period consistent with the model.
Difficulties: the origin of Ep is conventional and must be stated; the amplitude must stay moderate for the formula to apply.
Interpretation: the conservation observed is approximate, dissipation being weak but not zero.

Experiment 8: circular motion and change of direction

Question: can a motion at constant speed be accelerated?
Level: grades 11–12.
Duration: 1 h.
Medium: video of an object in steady rotation, filmed perpendicular to the plane of the circle.
Procedure: mark one full turn; display the trajectory, the speed, and the successive velocity vectors.
Quantities: position, magnitude and direction of velocity, angle, angular velocity.
Representation: circular trajectory with velocity vectors.
Model: v = Rω, centripetal acceleration directed towards the centre.
Expected result: constant magnitude, rotating direction.
Interpretation: here the acceleration reflects a change of direction only.
Extension: compare with the direct measurement by accelerometer and gyroscope, described in the accelerometer and gyroscope guide.

Experiment 9: collision between two objects

Question: what is conserved in a collision?
Level: grade 12.
Duration: 1 h 30.
Medium: video of two objects on a table or a track, filmed from above or from the side.
Procedure: mark each object in turn; obtain the velocities before and after the collision by linear regression on the straight portions; compare momenta and kinetic energies.
Quantities: velocities before and after, masses (measured separately).
Representation: x(t) of both objects on the same graph.
Model: conservation of momentum; conservation of kinetic energy in the elastic case only.
Expected result: momentum conserved within uncertainty; kinetic energy conserved or not depending on the nature of the collision.
Difficulties: friction on the table, motion leaving the plane after the collision.
Interpretation: distinguish elastic from inelastic collisions through the energy balance.
Conclusion not permitted: declaring a “perfectly elastic” collision without discussing the uncertainty.

Experiment 10: analysing a sports movement

Question: what does the physics of a technical movement reveal?
Level: grades 11–12, project work.
Duration: a project across several sessions.
Medium: video shot by the students.
Procedure: choose a movement, design the shot (plane of motion, calibration reference, frame rate), film, mark, analyse, write up.
Quantities: depending on the project — release velocity, trajectory, energy, launch angle.
Difficulties: success is determined by the design of the shot, not by the marking.
Interpretation: the student runs the whole process, from choosing the problem to the conclusion.
Resources: the kinematic analysis of the pole vault, 12 sports to study with a smartphone, and the 15 teacher projects.

Experiment 11: comparing video analysis with the accelerometer

Question: do two independent methods give the same result?
Level: grade 12.
Duration: 1 h 30.
Medium: one smartphone films, a second is attached to the object under study.
Procedure: record the accelerometer data and the video of the same motion simultaneously (a cushioned fall, a pendulum, a lift); compare the quantities they have in common.
Quantities: acceleration from video analysis, absolute and linear acceleration from the inertial sensor, period.
Representation: curves superimposed after synchronisation.
Expected result: agreement on periods and on characteristic instants; instructive discrepancies on acceleration values.
Interpretation: the two methods do not measure the same thing — the accelerometer measures the specific force experienced by the device, while video analysis reconstructs the motion in the laboratory frame. In free fall, the accelerometer reads close to zero while the video shows an acceleration of 9.8 m·s⁻²: this apparent disagreement is the most instructive result of the experiment.
Resource: the accelerometer and gyroscope guide.

Experiment 12: measuring your own marking uncertainty

Question: by how much do two markings of the same motion differ?
Level: grade 12, first year of higher education.
Duration: 1 h.
Medium: the same video, marked several times.
Procedure: have the same video marked by several students, or three times by the same student; export the positions; compute the standard deviation of the positions for each frame; deduce σ, then predict σ_v and σ_a using the formulas in section 4.3; compare with the scatter actually observed on the velocity and acceleration curves.
Quantities: positions, standard deviation, propagated uncertainties.
Representation: histogram of the deviations, prediction versus observation.
Model: σ_v = σ/(Δt√2), σ_a = σ√6/Δt² for central-difference differentiation.
Expected result: σ of the order of 1 to 3 pixels, and an acceleration scatter consistent with the predicted order of magnitude.
Interpretation: the student verifies the propagation of uncertainties experimentally, instead of simply being subjected to it.
Resource: the guide to understanding measurement uncertainty.

Part 10: FizziQ compared with other software

Several tools allow image-based kinematic analysis, and none is best in absolute terms. They answer different constraints: available equipment, level of the students, session length, budget, and the institution’s policy on smartphones. Here is an honest survey.

AviMéca is the historical video point-marking tool in French upper secondary schools. Free and running under Windows, it has trained several generations of teachers and is still installed in many classrooms. It is often paired with Regressi or a spreadsheet for data processing. Its main constraint is being tied to a Windows environment installed on fixed workstations, which rules out tablets and Chromebooks.

PhysMo is a free, education-oriented tool designed for simple video analysis. Its development appears to have stopped — the last published version dates from 2011 and depends on Java 1.6 — and it has remained little used. It is mentioned here for historical completeness, which is why it does not appear in the comparison table below.

Tracker, developed by Douglas Brown within Open Source Physics, is the free reference in this field. It is free, GPL-licensed, available for Windows, macOS, and Linux, and actively maintained. This should be said plainly: Tracker goes further than FizziQ on several counts — automatic object tracking, multiple reference frames, distortion correction, image filters, and above all dynamic modelling, that is, the ability to define a physical model (forces, initial conditions) and superimpose its simulation on the experimental data. It is a remarkable tool for the final years of secondary school and for higher education. Tracker is used mainly as a desktop application whose installer supplies its own Java environment — so there is normally no separate Java to install. A Tracker Online version, opening in the browser, also exists, but the desktop application remains the reference for advanced use. Its other constraints are a dense interface and documentation that is essentially English-language, and getting genuinely proficient generally takes longer than with a lighter-weight tool.

Vernier Video Analysis is a specialised, well-designed, multi-platform application, also available in a browser version. It is distributed under a paid institutional licence, which makes it an equipment purchase rather than a tool each student installs freely.

FizziQ Mobile stands out for the continuity between capture and analysis on the same device, the built-in library of videos and chronophotographs, the experiment notebook, and the fact that the app is free, requires no account, and collects no personal data. It also stands out for its explicit, pedagogically framed support for chronophotography — a dedicated mode, a built-in library, and direct continuity with video analysis and the experiment notebook — and for situating image analysis among the other methods of studying motion (inertial sensors, GPS, acoustic methods).

FizziQ Web brings the same analysis into a browser, with no installation, which addresses the very common case of an institution equipped with computers or Chromebooks and not permitting smartphones.

Criterion	AviMéca	Tracker	Vernier Video Analysis	FizziQ Mobile	FizziQ Web
Cost	Free	Free and open source	Paid licence	Free	Free
Installation	Windows	Desktop (Java included) + online version	Apps and browser	Mobile app	None, browser
Smartphone / tablet	No	No	Yes	Yes	No
Chronophotography	Limited	Possible	No	Dedicated mode	Dedicated mode
Film and analyse on the same device	No	No	Yes	Yes	No
Automatic object tracking	No	Yes	Partial	No	No
Dynamic modelling	No	Yes	No	No	No
Learning curve	Quick	Long	Quick	Very quick	Very quick

The characteristics of third-party software change over time; this table reflects the situation as of writing and is worth re-checking before any purchase or rollout.

In practice. For a quick introduction, a short session, fieldwork, or a class equipped with tablets, FizziQ Mobile or FizziQ Web are the most effective. For an in-depth final-year or specialist project involving comparison with a dynamic model, Tracker remains the most powerful tool. The two approaches are not mutually exclusive: filming and learning the method with FizziQ, then going deeper with Tracker on the same video, is a coherent progression.

Common errors and misconceptions

“The trajectory is the x(t) curve.” False. The trajectory is the set of successive positions in the plane, the curve (x(t), y(t)), which carries no time information along the path; it can only be written as y(x) when each x-value corresponds to a single y-value. Correct approach: name both axes before interpreting a graph. For a projectile, the trajectory and y(t) are two different parabolas, and x(t) is a straight line.

“The velocity measured is the instantaneous velocity.” Inaccurate. All that is measured are average velocities over short intervals, which estimate the instantaneous velocity. Correct approach: speak of an estimated instantaneous velocity, and know that the quality of the estimate depends on Δt.

“The speed is constant, therefore the velocity vector is constant.” False. In uniform circular motion the magnitude is constant while the direction changes continuously: the velocity vector varies, so the acceleration is not zero.

“The velocity is zero, therefore the acceleration is zero.” False. At the top of a vertical throw the velocity vanishes while the acceleration is still g. The same reasoning applies at the extremes of a pendulum’s swing.

“The scale can be taken from any visible object.” False, and costly. The calibration reference must be in the plane of the motion, at the same distance from the camera as the object. A ruler on the back wall falsifies every length, every velocity, and every acceleration, without any graph giving a hint.

“You can film slightly off-axis, it evens out.” False. Nothing compensates for parallax and perspective: they distort the trajectory non-uniformly, which looks like a physical effect.

“The frame rate is always the one the file declares.” False for slow motion. A file exported at 30 fps may have been shot at 240 fps: velocities are then 8 times too small and accelerations 64 times too small. Check: film a free fall and verify that you recover about 9.8 m·s⁻².

“Filming faster always gives better results.” False for derived quantities. Reducing Δt amplifies marking noise: velocity degrades as 1/Δt and acceleration as 1/Δt². Correct approach: film fast to obtain sharp and sufficiently numerous frames, but mark points at a suitable interval.

“The more points you add, the more precise the analysis.” False as stated. Adding points over a given duration helps if a model is then fitted; tightening the interval between points degrades point-by-point velocities and accelerations instead.

“You read g off the acceleration curve.” Best avoided. That curve is the noisiest of all. Correct approach: fit a parabola to y(t), which improves the uncertainty by a factor of several tens on exactly the same data.

“A smoothed signal is more accurate.” False. Smoothing improves readability, attenuates peaks, and delays rapid variations. On a bounce or an impact, it distorts the very event you are trying to measure.

“You can change the marking feature partway through.” False. Switching from the edge to the centre of the object introduces a systematic offset that appears as a spurious jump in velocity. The same feature must be marked from the first point to the last.

“The potential energy displayed is the object’s true energy.” False. It depends on a conventional origin chosen by the user; only its variations carry physical meaning. Likewise, the mass used for energies is entered by the experimenter: it is not a measurement taken from the video.

“Fluctuations in the curves are physical phenomena.” Often false. Before interpreting a wobble in the acceleration, you need an estimate of the expected differentiation noise (Experiment 12). A motion whose acceleration is known to be zero serves as a reference test.

“Video analysis measures forces.” False. It is purely kinematic: it yields positions, and by calculation velocities and accelerations. Forces are then inferred through dynamical reasoning.

Frequently asked questions

How do you measure a velocity from a video? You set a scale from an object of known length placed in the plane of the motion, check the video’s frame rate, then mark the object’s position frame after frame. The software converts pixels to metres and frame numbers to seconds, then computes velocity by numerical differentiation of the positions. For a constant velocity, the most reliable method is the slope of a linear regression on x(t).

What is the difference between video analysis and chronophotography? Video analysis works from a sequence of frames separated by an interval written into the file; chronophotography works from a single image carrying an object’s successive positions, whose time interval is never contained in the image and must be supplied. Video lets you choose and correct the marking; chronophotography makes the motion visible at a single glance, which makes it an excellent entry point in lower secondary.

Which frame rate should I choose? The one that makes the object cover, between two retained points, a distance clearly larger than the marking uncertainty while still describing the motion properly. As an order of magnitude: 30 fps suits a fall or a walk, 120 to 240 fps are useful for an impact or a fast sports movement. At high frame rates you should then mark one frame in several rather than every frame.

Why is the acceleration curve so noisy? Because acceleration is not measured but obtained by differentiating the positions twice, and each differentiation divides by Δt and amplifies the marking error. A 3 mm position error becomes, at 30 fps and without smoothing, an error of nearly 7 m·s⁻² on the acceleration.

How do I get a good value of g from a video? By fitting a parabola to the vertical positions rather than reading the acceleration curve. The fit uses all the points at once and improves the uncertainty by a factor of several tens on the same data.

Why are my velocities far too low? Almost always a frame-rate problem on a video shot in slow motion: the file plays back at 30 fps although it was recorded at 120 or 240 fps. Velocities are then 4 or 8 times too small. The check is to analyse a free fall and verify that you recover about 9.8 m·s⁻².

How do I avoid parallax? By placing the camera facing the middle of the trajectory, with the optical axis perpendicular to the plane of the motion, and far enough away that the motion stays in the central zone of the image.

Where should the ruler used for the scale be placed? In the plane of the motion, at the same distance from the camera as the object. A reference placed in front of or behind that plane introduces a systematic error on every quantity, invisible on the graphs.

Can I use a video filmed with any smartphone? Yes, in the vast majority of cases. A resolution of 720p is enough; what matters more is a steady device, good lighting, a well-contrasted object, and knowing the real frame rate. Slow-motion performance and the extent of rolling shutter do, however, vary a great deal between models.

Can I analyse a video on a computer? Yes, with FizziQ Web, which runs in the browser with no installation, on computers and Chromebooks alike, with mouse marking, a built-in spreadsheet, and export.

What is the difference between FizziQ and FizziQ Web? FizziQ is the mobile app: it lets you film and analyse on the same device, in class or in the field, and works offline once installed. FizziQ Web is a separate application that opens in a desktop browser: it offers mouse marking, a large screen, a scientific spreadsheet, and report writing on a keyboard. The calculated quantities are the same; the interfaces are different.

What free alternative is there to AviMéca? FizziQ Web meets the same need with no installation and runs on any recent computer or Chromebook, including outside a Windows environment. FizziQ Mobile covers tablets and smartphones. Tracker is the other free alternative, more powerful but requiring installation and a longer learning period.

What is the difference between FizziQ and Tracker? Tracker is more complete on automatic tracking, multiple reference frames, and above all dynamic modelling, but it installs on a computer and generally takes longer to get to grips with. FizziQ favours a quick start and a workflow suited to classroom sessions; it is free, runs on mobile and in a browser, includes a video library and an experiment notebook, and treats chronophotography as a mode in its own right. The two are complementary: discover with FizziQ, go deeper with Tracker.

Can I work on a Chromebook? Yes, with FizziQ Web in the browser. This is the recommended solution for institutions equipped with Chromebooks or not permitting smartphones in class.

Do I need to install software on the computer? Not for FizziQ Web, which is used directly in the browser. The FizziQ app itself installs on smartphones and tablets.

Can I compute an energy from a video? Yes, provided you supply the object’s mass, which the video does not measure, and choose an origin for the potential energy. The displayed values of Ep and Em depend on that convention: only their variations carry physical meaning.

Video analysis or accelerometer: which should I choose? The accelerometer measures what the device itself experiences and suits cases where the smartphone can be attached to the object under study. Video analysis reconstructs the trajectory of a separate object in the laboratory frame, and suits cases where the device must stay still. The accelerometer and gyroscope guide compares the four methods of studying motion available with a smartphone.

Conclusion

A video becomes a measuring instrument as soon as two calibrations are under control: a reference length in the plane of the motion, and a time interval between frames. Everything else — trajectory, velocity, acceleration, energy — follows by calculation.

It is precisely because those quantities are calculated rather than measured that the method demands rigour. Position is solid, velocity is reliable, acceleration is fragile. A teacher who has grasped this hierarchy avoids most of the disappointments: they have students fit models to positions rather than read values off noisy curves, have them check the frame rate with a free fall, and have them place the calibration reference in the plane of the motion.

Image-based analysis holds a special place among the methods of studying motion: it reconstructs a complete trajectory in the laboratory frame without attaching any sensor to the object under study. It combines naturally with the others — inertial sensors, GPS, acoustic timing — and it is from that confrontation that genuine experimental practice emerges.

The recommended starting point takes ten minutes: open a free-fall video from the FizziQ library, calibrate it, mark the points, then fit a parabola to the positions. If you get 9.8 m·s⁻², everything else is within reach.

To go further on fizziq.org: the product overview of kinematic analysis, the library of kinematics videos and the library of chronophotographs, FizziQ Web for analysis on a computer or Chromebook, the accelerometer and gyroscope guide, the complete guide to smartphone sensors, the guide to sound, the guide to measurement uncertainty, the article on using chronophotography in lab sessions, the kinematics activities, and the glossary entry on kinematics.

Sources and references

FizziQ documentation: the kinematic analysis overview page, FizziQ Web, and the video and chronophotograph libraries.

Technical and pedagogical references:

Brown, D. — Video Modeling: Combining Dynamic Model Simulations with Traditional Video Analysis, AAPT Summer Meeting, 2008, and the documentation for the Tracker software (Open Source Physics).
Wee, L. K. & Lee, T. L. — Video Analysis and Modeling Tool for Physics Education, 2012.
Ramli, M., Chan, K. & Fen, W. — Study of Simple Pendulum Using Tracker Video Analysis and High Speed Camera, Solid State Science and Technology.
Savitzky, A. & Golay, M. J. E. — Smoothing and Differentiation of Data by Simplified Least Squares Procedures, Analytical Chemistry, 1964, for the principle of differentiation by moving polynomial fit.
Marey, É.-J. — Le mouvement, 1894, for the foundations of chronophotography.
BIPM — Guide to the Expression of Uncertainty in Measurement (GUM), for the propagation of uncertainties.
Éduscol physics and chemistry curricula and resources (French Ministry of Education).

Introduction: how does a video become a measurement?

Table of contents

Part 1: what is image-based kinematic analysis?

1.1 Kinematics and dynamics

1.2 The system under study and the representative point

1.3 Frame of reference and coordinate system

1.4 Trajectory, x(t), and y(t): three different graphs

1.5 An old method, a recent tool

Part 2: video or chronophotography?

2.1 Two media, one principle

2.2 What each medium offers

Part 3: how an image becomes a measurement

3.1 Spatial calibration: from pixels to metres

3.2 Temporal calibration: Δt = 1/f

3.3 Origin and axes

3.4 What is measured, what is calculated

3.5 The slow-motion trap: the error you cannot see

Part 4: from position to velocity and acceleration

4.1 Average velocity and instantaneous velocity

4.2 Estimation by central differences

4.3 Why is acceleration always noisier than position?

4.4 The high-frame-rate paradox

4.5 What FizziQ does

4.6 The right method: fit a model to the positions

Part 5: shooting a usable video

5.1 The ten rules

5.2 Four optical defects worth knowing

5.3 Precautions

5.4 Filming is not always necessary

Part 6: two FizziQ tools, mobile and desktop

6.1 FizziQ on smartphone and tablet

6.2 FizziQ Web on a computer

6.3 Which environment to choose?

Part 7: performing a kinematic analysis with FizziQ

7.1 Opening the kinematic analysis

7.2 Choosing a video or a chronophotograph

For a video analysis

For a chronophotograph

7.3 Setting the scale and the coordinate system

Setting the spatial scale

Choosing the origin and axes

7.4 Checking the time parameters

For a video analysis

For a chronophotograph

7.5 Marking the motion

7.6 Examining the results

7.7 Working with the data in the experiment notebook

7.8 Creating a chronophotograph from a video

7.9 Tips for a successful analysis

Stabilise the camera

Film perpendicular to the motion

Place a reference object in the plane of the motion

Use a contrasting background

Light the scene properly

Avoid motions that are too fast or too small

Limit the length of the sequence

7.10 A recommended first exercise: studying a free fall

7.11 FizziQ Mobile or FizziQ Web: which to choose?

Part 8: reading the graphs

8.1 Uniform straight-line motion

8.2 Uniformly accelerated straight-line motion

8.3 Free fall

8.4 Projectile motion

8.5 Uniform circular motion

8.6 Pendulum

8.7 Bounces

Part 9: precision, uncertainties, and limits

9.1 The uncertainty budget of a video analysis

9.2 No, adding points does not always improve precision

9.3 The limits of the model

Twelve experiments using video and chronophotography

Experiment 1: reading a motion from a chronophotograph, without calculation

Experiment 2: uniform straight-line motion and differentiation noise

Experiment 3: measuring g by parabolic fit

Experiment 4: decomposing projectile motion

Experiment 5: quantifying friction

Experiment 6: energy dissipation during bounces

Experiment 7: pendulum, period, and energy exchange

Experiment 8: circular motion and change of direction

Experiment 9: collision between two objects