A2 Daily A Level Physics question
A car passes point X at 20 m/s and, 100 m further on at point Y, it is moving at 15 m/s, having braked uniformly between X and Y. If the driver continues to brake at the same rate after Y, approximately how much further will the car travel before coming to rest?
Answer
The correct answer is D.
Correct: D — about 130 m. A assumes stopping distance is proportional to speed (taking 15/20 of 100 m), but with constant deceleration the change in speed squared is what scales with distance. B assumes equal distance gives equal drop in speed, whereas equal distance actually gives equal drop in speed squared, so more than 100 m is needed from 15 m/s to reach zero. C treats speed drop per metre as constant (5 m/s per 100 m, so 15 m/s needs 300 m), but under uniform deceleration it is the drop in v^2 that is constant per metre. D uses the correct proportionality: over 100 m, v^2 drops by 400 − 225 = 175; to go from 15 m/s to rest requires a further drop of 225, so extra distance ≈ (225/175) × 100 ≈ 1.29 × 100 ≈ 130 m.