AS Daily A Level Physics question
In a lab trolley experiment, the trolley starts from rest and moves with constant acceleration a for time t. In a second run you double the acceleration to 2a and let it run for twice the time, 2t. Using a velocity–time graph idea, by what factor does the displacement change compared with the first run?
Answer
The correct answer is A.
Correct: A — It becomes eight times larger. A is correct because from rest the v–t graph is a triangle with area 1/2 × base × height = 1/2 × t × (a t), so doubling both a and t multiplies the area by 2 × 2^2 = 8. B is wrong because a factor of 4 would apply if only time were doubled with acceleration unchanged. C is wrong because displacement does not scale just linearly with one doubled quantity here; both height and base increase, giving more than a factor of 2. D is wrong because changing both acceleration and time cannot leave the displacement the same.