Equations of uniformly accelerated motion
4 marks · NormalA student investigates the motion of a remote-controlled car along a straight runway. The car accelerates uniformly from rest. The student records the following data:
| Distance travelled (s) / m | Final speed (v) / m/s |
|---|---|
| 0.0 | 0.0 |
| 1.5 | 3.9 |
| 4.0 | 6.7 |
| 7.0 | 9.2 |
Using the data for s = 7.0 m, calculate the car’s acceleration.
State the initial speed of the car for this 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) 6.05 m/s² · must show Uses v^2 = u^2 + 2as, u = 0, Correctly rearranges and substitutes, Final answer to reasonable precision
(b) 0 m/s · must show Identifies initial speed as zero
Common mistakes: Confusing v with u; Missing units; Incorrect denominator arrangement
Show mark scheme and worked solution
Marking points
M1 (a) · 1 mark · States/uses the correct equation for uniform acceleration: v^2 = u^2 + 2as (with u = 0).
M2 (a) · 1 mark · Substitutes correct values: v = 9.2 m/s, s = 7.0 m, u = 0. (follow-through)
A1 (a) · 1 mark · Evaluates a = 6.05 m/s² (allow 6.1 within tolerance). (follow-through)
B1 (b) · 1 mark · States initial speed is 0 m/s.
Worked solution
a) For s = 7.0 m, final speed v = 9.2 m/s, initial speed u = 0 m/s.
b) The car starts from rest, so initial speed is 0 m/s.