AS Daily A Level Physics question
In a lab, a trolley starts from rest and its velocity–time graph is a straight line while a small fan pushes it. It reaches 3.0 m/s in 4.0 s. The fan speed is then reduced so that the straight-line gradient of the velocity–time graph is halved, but the trolley still reaches 3.0 m/s. What is the new time to reach 3.0 m/s?
Answer
The correct answer is A.
Correct: A — 8.0 s. A straight-line v–t graph has acceleration equal to its gradient; halving the gradient halves the acceleration, so to reach the same change in velocity the time must double: 2 × 4.0 s = 8.0 s. A — Correct because time is inversely proportional to acceleration for a fixed change in velocity, so halving acceleration doubles time. B — Incorrect: this assumes time halves when the gradient halves, but time increases when acceleration decreases for the same speed change. C — Incorrect: time would stay the same only if the acceleration (gradient) stayed the same. D — Incorrect: adding 2.0 s treats the change as a fixed offset; here the change is proportional (a halved gradient requires double the time).