Equations of uniformly accelerated motion
4 marks · NormalA student investigates the motion of a toy trolley moving along a straight track. She records the following data:
| Time / s | Speed / m/s |
|---|---|
| 0.0 | 0.0 |
| 1.0 | 0.7 |
| 2.0 | 1.4 |
| 3.0 | 2.1 |
| 4.0 | 2.8 |
Calculate the trolley's acceleration from the data.
Suggest a reason why the acceleration might not be exactly constant in a real experiment.
Work this out on paper, then compare with the answer and worked solution below. With a free account you can submit written answers for marking.
Show answer
(a) 0.7 m/s^2 · must show Uses two data points or average rate, Correct arithmetic
(b) Friction or air resistance affects the motion; surface roughness or uneven track changes the acceleration. · must show Mentions friction, resistance, or uneven surface, Explanation linked to changing acceleration
Common mistakes: Incorrect interval chosen for calculation; No reason or vague reason for b
Show mark scheme and worked solution
Marking points
M1 (a) · 1 mark · Correct substitution into a = (v - u) / t using suitable data from table.
A1 (a) · 1 mark · Correct numerical answer for acceleration (0.7 m/s², accept 0.65–0.75). (follow-through)
B1 (b) · 1 mark · Identifies a valid factor affecting real acceleration (friction, air resistance, uneven track, etc.).
B2 (b) · 1 mark · Gives brief explanation of how this factor causes acceleration to change.
Worked solution
a) Use first and last data points: a = (2.8 - 0.0) / (4.0 - 0.0) = 2.8 / 4 = 0.7 m/s²
b) The acceleration might not be exactly constant because friction between the trolley and the track, or air resistance, could affect the motion, causing the acceleration to decrease over time.