Uniform rectilinear movement

This activity allows students to understand the concept of Galilean frame of reference and uniform rectilinear motion. It develops the ability to experimentally verify the conditions of an ideal movement.

Newton's first law of motion, the principle of inertia, states that an object in motion continues at constant velocity in a straight line unless acted upon by a net external force. This deceptively simple statement defines the most fundamental type of motion in physics: uniform rectilinear motion (URM). In practice, achieving true URM is surprisingly difficult. Walking in a straight line at constant speed requires continuous muscular adjustment to counteract friction, air resistance, and the natural tendency to veer. This experiment challenges students to attempt URM using their own bodies and to use FizziQ sensors to evaluate how well they succeed. The accelerometer should read zero (no change in velocity) during perfect URM, while the GPS should show a constant speed. By comparing different sensor methods and observing the inevitable deviations from the ideal, students develop a concrete understanding of what a Galilean reference frame means and why Newton's first law is both profound and practically unattainable.

Activity overview:

The student uses FizziQ sensors to test whether it is possible to maintain a uniform rectilinear movement while walking. By recording acceleration or GPS position data during a movement in a straight line, the student analyzes the graph obtained to determine if the movement is truly uniform and then reflects on the difficulties and the most appropriate instruments to achieve and verify this type of movement.

Level:

Middle school

FizziQ

Author:

Duration (minutes) :

25

What students will do :

- Attempt to walk at constant velocity in a straight line and record sensor data
- Use the accelerometer to detect deviations from zero acceleration (the URM condition)
- Use GPS position data to evaluate the straightness and constancy of the motion
- Understand the concept of a Galilean reference frame and Newton's first law
- Identify the forces that prevent perfect URM in everyday motion

Scientific concepts:

- Uniform rectilinear movement
- Galilean reference frame
- Zero acceleration
- Inertia
- Principle of relativity

Sensors:

- Accelerometer (linear acceleration)
- GPS (position and speed tracking)

Material needed:

- Smartphone with the FizziQ application
- A clear outdoor space for walking in a straight line
- FizziQ experience notebook

Experimental procedure:

Find a straight, flat, open space at least 50 meters long (a running track, corridor, or sidewalk).
Open FizziQ and select the Linear Acceleration X sensor (forward-backward axis) and, if available, add GPS Speed in Duo mode.
Start recording and stand still for 5 seconds to establish a zero-acceleration baseline.
Begin walking in a straight line at the most constant speed you can maintain. Walk for at least 30 seconds or 50 meters.
Stop walking and stand still for another 5 seconds.
Stop recording and examine the acceleration graph. During perfect URM, it should show zero acceleration throughout the walking phase.
Observe the reality: the graph will show oscillations from each step and possible trends from speed changes.
If GPS data is available, examine the speed versus time graph. How constant was your walking speed?
Calculate the average acceleration during the walking phase. For good URM, this should be very close to zero.
Calculate the standard deviation of the acceleration during walking. This quantifies how far from ideal URM you achieved.
Try again, this time trying to walk more smoothly. Can you reduce the acceleration fluctuations?
Discuss: what forces prevent you from achieving perfect URM? What would a truly inertial reference frame look like?

Expected results:

The acceleration graph during walking will show periodic oscillations of approximately ±1-3 m/s² at the step frequency (about 1.5-2 Hz), superimposed on a near-zero average. The GPS speed will show fluctuations of ±0.2-0.5 m/s around a mean walking speed of typically 1.2-1.5 m/s. The average acceleration over the entire walking phase should be close to zero (typically ±0.1 m/s²), confirming that the overall motion approximates URM even though individual steps deviate. Students should observe that the standing phases show lower acceleration noise than the walking phase, and that smooth, deliberate walking produces smaller fluctuations than hurried walking.

Scientific questions:

- What does Newton's first law predict about an object in uniform rectilinear motion?
- Why is it impossible to achieve perfect URM while walking?
- What forces act on your body during walking? Do they cancel out on average?
- What is a Galilean reference frame, and how does it relate to URM?
- How would URM differ in outer space, where friction and gravity are absent?
- Why do the acceleration oscillations during walking not average to zero over a single step?

Scientific explanations:

Uniform rectilinear motion (MRU) is characterized by a straight line trajectory and constant velocity, which implies zero acceleration. It is the natural movement of a body when no force is exerted on it, as Newton formulated it in his first law (principle of inertia).

A frame of reference in which this principle is verified is called a Galilean frame of reference. This experiment allows you to explore these fundamental concepts of classical mechanics.

To check if a movement is uniform rectilinear, several FizziQ sensors can be used: 1) The accelerometer: in a perfect MRU, the acceleration should be zero. Any variation indicates acceleration or deceleration; 2) GPS: by tracing the position over time, we can check the linearity of the movement and the constancy of the speed.

In practice, performing a true MRU while walking is surprisingly difficult because human walking is naturally oscillatory and jerky. Each step involves a phase of acceleration and deceleration.

This difficulty illustrates why perfect MRUs are rare in nature and generally limited to brief periods. The Galilean principle of relativity states that the laws of mechanics are identical in all Galilean frames of reference.

This explains the strange sensation evoked in the activity: in a high-speed MRU train, we do not "feel" the movement because all the physical laws apply there exactly as in a stationary frame of reference. It is only the acceleration that we perceive, hence the strangeness of the moments when we have the impression of being still even though we are moving at high speed.

This experience thus makes it possible to make the link between a fundamental theoretical concept and a daily sensory experience.

Extension activities:

Frequently asked questions:

Q: The accelerometer never shows exactly zero during walking. Does this mean URM is impossible?
R: True URM requires zero net force, which is impossible for a human body that must continuously push against friction and gravity. The step-by-step oscillations reflect the periodic push-off and landing of each step. URM is an idealization that real motion can only approximate.

Q: The GPS speed fluctuates a lot. Is GPS precise enough for this experiment?
R: GPS speed has a typical precision of ±0.3-0.5 m/s, which is comparable to the actual speed variations during walking. It is useful for confirming approximately constant speed but not for detecting small variations.

Q: Why does the average acceleration come out close to zero even though individual values fluctuate?
R: Each step involves a forward push (positive acceleration) followed by braking (negative acceleration). If the average speed is constant, these positive and negative phases cancel out over time, giving a near-zero average.

Q: Would a hovercraft achieve better URM than walking?
R: Yes, a hovercraft eliminates ground friction, allowing it to glide at nearly constant velocity once propulsion stops. However, air resistance would still gradually decelerate it.