Coaching Centre
Investigating motion with technology
The Module 1 motion practical: measuring velocity and acceleration with light gates, motion sensors, video analysis and phone apps, processing data into graphs, and evaluating validity, reliability and accuracy.
A stopwatch in a human hand has a reaction time of about 0.2 s. A light gate times to a tenth of a millisecond. When a trolley takes half a second to roll down a ramp, that difference decides whether your result is useful or meaningless.
In Year 10 you timed motion with ticker-tape and stopwatches. The Year 11 practical asks you to choose a suitable technology, collect your own data, and use it to find velocity and acceleration. Exam questions test the method, the processing and the evaluation, so this page covers all three.
Choosing a technology
| Technology | What it measures directly | Strengths | Limitations |
|---|---|---|---|
| Light gate + data logger | time a card blocks an infrared beam; time between gates | very precise timing (0.1 ms); automatic | gives average velocity over the card width, not true instantaneous velocity |
| Ultrasonic motion sensor | distance, from the echo time of ultrasound pulses | draws position–time and velocity–time graphs live | needs a large flat target; stray echoes; minimum range about 15 cm |
| Video analysis (phone, Tracker) | position in each frame at a known frame rate | whole motion recorded; cheap | parallax; motion blur; frame rate limits time resolution |
| Phone accelerometer app | acceleration directly | no extra equipment | noisy data; phone must be fixed to the object |
| Ticker-timer | dots at fixed time intervals (often 50 per second) | simple, permanent record | friction from the tape; dots hard to read at low speed |
Light gates: how velocity is measured
A light gate is an infrared beam aimed at a sensor. While the card on the trolley blocks the beam, the logger times it. The velocity is then
$$v = \frac{\text{card width}}{\text{time the beam is blocked}}$$This is an average velocity over the time the card passes. If the trolley is accelerating, it is a little faster at the end of the card than at the start. A narrower card gives a value closer to the instantaneous velocity, but the time is shorter and the percentage timing uncertainty is larger, so there's a trade-off.
With two gates, the logger also records the time between them, and the acceleration follows:
$$a = \frac{v_2 - v_1}{t} \qquad \text{or} \qquad a = \frac{v_2^2 - v_1^2}{2s}$$where $s$ is the distance between the gates. The second form comes from 1D.
- Use the default set-up (10°, 10 cm card, gates at 30 cm and 80 cm) and release the trolley. The model acceleration is $9.8\sin 10^\circ = 1.70$ m/s², but the logger calculates only about 1.62 m/s². Each gate reads 1.089 m/s and 1.698 m/s, higher than the true speeds as the card arrives (1.010 and 1.650 m/s). Why?
- Change to the 1 cm card and release again. Now $v_1$ is within about 1% of the true speed. But the blocking times are only a few milliseconds, so a 0.1 ms timing error matters more. Release it a few times: how much does the calculated acceleration vary?
- Run trials at 5°, 10°, 15° and 20° with the 1 cm card and record the accelerations. Plot $a$ against $\sin\theta$ and find the gradient.
- Turn on friction. Is this a random or a systematic error?
Motion sensors and video
A motion sensor sends out ultrasound pulses and times the echo. Distance = $\tfrac12 \times$ speed of sound × echo time (half, because the sound goes there and back). Software then calculates velocity from successive positions and plots $s$–$t$ and $v$–$t$ graphs. The gradient of the $v$–$t$ graph gives the acceleration directly.
For video analysis, film the motion side-on against a metre rule, with the camera far away and level with the object to reduce parallax. Step through the frames: at 30 frames per second, each frame is $\tfrac{1}{30}$ s later. Programs such as Tracker plot the data for you.
Processing the data
A 5.0 cm card blocks gate 1 for 0.0410 s and gate 2 for 0.0250 s. The time between the gates is 0.480 s. Find the acceleration.
Plotting is better than a single calculation. A $v$–$t$ graph from a motion sensor or video should be a straight line for uniform acceleration; its gradient is $a$. A line of best fit averages out random errors, and an intercept that isn't where you expect is a sign of a systematic error.
Validity, reliability and accuracy
- Validity: does the method test what it claims? Controlled variables held constant, the trolley released (not pushed), the card perpendicular to the beam.
- Reliability: do repeats agree? Five trials per angle and a small spread mean reliable data.
- Accuracy: how close is the result to the accepted or expected value? Compare the gradient with 9.8 m s⁻² as a percentage difference.
| Problem | Type | Fix |
|---|---|---|
| Friction and air resistance reduce the acceleration | systematic | low-friction track, or compensate by tilting until the trolley rolls at constant speed |
| Card wider than needed, so $v$ is an average | systematic | narrower card, or calculate velocity at the mid-time |
| Trolley pushed slightly on release | random | stop block and release by lifting a barrier; repeat trials |
| Angle measured roughly with a protractor | random or systematic | measure height and length and use $\sin\theta = h/L$ |
Test yourself
A 2.0 cm card blocks a light gate for 12.5 ms. The trolley's velocity is
$0.020 \div 0.0125 = 1.6$ m s⁻¹.
Why does a narrower card give a better estimate of instantaneous velocity?
The measurement is an average over the blocking time; a shorter time means less change in velocity during it. (The percentage timing uncertainty actually gets worse.)
A motion sensor measures an echo time of 6.0 ms. With the speed of sound 340 m s⁻¹, the distance to the trolley is
$\tfrac12 \times 340 \times 0.0060 = 1.02$ m. The sound travels there and back.
A student's measured accelerations are all about 8% below $g\sin\theta$. The best improvement is to
A consistent shortfall is systematic, most likely friction. Repeating doesn't remove it.
Label the light-gate set-up.
Classify each source of error.
A light gate measures the time a card blocks an beam. The velocity is the card divided by that time, which gives an velocity. With two gates, acceleration is the change in velocity divided by the between the gates. For a trolley on a frictionless ramp, the acceleration is $g\,$.
Describe a valid and reliable method, using a technology of your choice, to measure the acceleration of a trolley rolling down a ramp. Include how the data are processed and one way to improve accuracy.
Set up a ramp at a fixed angle with two light gates about 50 cm apart, connected to a data logger. Measure the width of the card on the trolley with calipers. Keep the trolley, card, angle, release point and gate positions the same for every trial.
Release the trolley from rest against a stop block so it isn't pushed. The logger records the time the card blocks each gate and the time between the gates. Repeat five times and average the times; repeats that agree closely show the data are reliable.
For each gate, $v = $ card width ÷ blocking time. The acceleration is $a = (v_2 - v_1)/t$, where $t$ is the time between gates. Compare with the expected $g\sin\theta$.
To improve accuracy, reduce the systematic error from friction by using an air track or low-friction wheels, and use a narrow card so each measured velocity is closer to the instantaneous value.