AS Daily A Level Physics question
A dynamics trolley on a smooth track is brought to rest by a magnetic brake that provides a constant deceleration. In one test it starts at 1.5 m/s and stops in 0.75 s. If the same brake is used but the trolley starts at 3.0 m/s, what happens to the stopping distance compared with the first test?
Answer
The correct answer is A.
Correct: A — It is four times larger. For the first run, a = 1.5/0.75 = 2.0 m s−2; with constant deceleration, stopping distance scales as u^2 (since s = u^2/(2|a|)), so doubling u from 1.5 to 3.0 m/s makes s four times bigger. A This follows from s ∝ u^2 at fixed deceleration (or by noting time to stop doubles and average speed during braking also doubles, so distance ×4). B Assumes distance scales linearly with initial speed; under constant deceleration it scales with the square of speed, so doubling u does not merely double s. C Mixes up the square-root relationship, as if u ∝ √s; here it is s that is proportional to u^2, not u to √s in the comparison. D Double-counts effects to get an exaggerated factor (e.g. incorrectly compounding time and speed changes); with constant a, the correct scaling is exactly ×4, not ×8.