AS Daily A Level Physics question
In a controlled dry-road brake test, the same car is brought from speed u to rest using the same maximum braking force each time (so the deceleration magnitude is the same in both runs). In the second run the initial speed is increased by 50%. Which statement must be true about how the stopping distance and stopping time change?
Answer
The correct answer is C.
Correct: C — Stopping distance increases by a factor of 2.25; stopping time increases by a factor of 1.5. With the same deceleration, time to stop is proportional to the initial speed, while stopping distance is proportional to the square of the initial speed; increasing speed by 1.5 scales time by 1.5 and distance by 1.5^2 = 2.25. A assumes both quantities scale linearly with speed, ignoring that distance depends on speed squared. B swaps the dependencies, treating distance as linear and time as quadratic. C matches the correct proportionalities for constant deceleration. D assumes both quantities depend on speed squared, but the stopping time is only linear in the initial speed.