AS Daily A Level Physics question
In a lab, a trolley on a smooth horizontal track starts from rest and accelerates uniformly. It travels 1.6 m in the first 2.0 s. If the same acceleration continues, how far does it travel during the next 2.0 s (from t = 2.0 s to t = 4.0 s)?
Answer
The correct answer is D.
Correct: D — 4.8 m. With uniform acceleration from rest, distance scales with the square of time: from 0–2 s to 0–4 s the total distance increases by a factor of 4 (1.6 m to 6.4 m), so the distance in the next 2 s is 6.4 − 1.6 = 4.8 m. A 1.6 m assumes equal distances in equal time intervals as if speed were constant, but distance per interval increases as the trolley speeds up. B 3.2 m treats the instantaneous speed at 2.0 s as the average speed over 2.0–4.0 s, underestimating the increasing speed during that interval. C 6.4 m is the total distance by 4.0 s, not just the distance covered between 2.0 s and 4.0 s. D 4.8 m follows the s ∝ t^2 reasoning or triangle areas under a velocity–time graph: the extra area from 2–4 s is three times the first-2-s distance.