AS Daily A Level Physics question
A lab trolley is brought to rest by the same magnetic brake in two trials. In both, the brake provides the same constant deceleration until the trolley stops. In trial 1 the starting speed is 0.80 m s−1 and the stopping distance is s1. In trial 2 the starting speed is 1.20 m s−1. Which statement about s2, the stopping distance in trial 2, must be true?
Answer
The correct answer is B.
Correct: B — s2 is 2.25 times s1. With the same constant deceleration, stopping time is proportional to the initial speed, so stopping distance scales with speed squared; the speed ratio is 1.20/0.80 = 1.5, so distance scales by 1.5^2 = 2.25. A This assumes distance scales linearly with initial speed, ignoring that the longer stopping time at higher speed also increases distance, giving a square dependence. B This matches the square scaling for constant deceleration: both higher initial speed and longer stopping time contribute, giving 2.25×. C This overestimates by treating the effect as more than quadratic (or by compounding factors incorrectly); the correct factor is 1.5^2, not 1.5×2. D Same deceleration does not imply the same stopping distance; a higher initial speed means a longer time to stop and therefore a greater distance.