AS Daily A Level Physics question
A cyclist on level ground brakes so that the deceleration is the same each time (uniform and constant). If the initial speed is doubled, what happens to the stopping distance and the stopping time until rest?
Answer
The correct answer is C.
Correct: C — Stopping distance quadruples; stopping time doubles. With the same constant deceleration, the time to stop is proportional to the initial speed (t ∝ u), while the stopping distance depends on the square of the initial speed (s ∝ u²), so doubling u doubles t and quadruples s. A assumes both quantities scale linearly with speed; time does, but distance does not. B assumes distance scales linearly and that time is independent of speed, which contradicts uniform deceleration where t ∝ u. C matches the correct proportionalities for constant deceleration. D correctly identifies the quadratic change in distance but incorrectly claims the stopping time is unchanged.