AS Daily A Level Physics question
On a dry test track, the same car makes two emergency stops: Run 1 from speed v, Run 2 from speed 2v. The driver’s reaction time is the same non‑zero value in both runs. Once the brakes are applied, the car experiences the same constant-magnitude deceleration in both runs, opposite to the direction of motion (take forward as positive). Comparing the total stopping distances (reaction distance plus braking distance), which statement must be true for Run 2 relative to Run 1?
Answer
The correct answer is B.
Correct: B — More than twice but less than four times as long. Reaction distance doubles when speed doubles, while braking distance (under the same constant deceleration, opposite to motion) scales with the square of speed, so it quadruples; with non‑zero reaction time and finite deceleration, the combined total must lie strictly between a factor of 2 (reaction-dominated limit) and 4 (zero‑reaction‑time limit). A assumes everything scales linearly with speed and ignores that the braking part grows faster than reaction distance. B correctly reflects that one contribution doubles and the other quadruples, so the total cannot be exactly 2× or 4×. C treats the whole stopping distance as if it were only the braking part (as if reaction time were zero). D would require the total to grow faster than the braking term alone, which cannot happen if the deceleration is the same and reaction time is unchanged.