AS Daily A Level Physics question
In a flat-ground cycling drill, two students cover a 10 s interval. Student A starts from rest and increases speed uniformly for the first 4.0 s, then keeps that speed constant for the remaining 6.0 s. Student B starts at 3.0 m s⁻¹ and also increases speed uniformly for the first 4.0 s, then keeps that speed constant for 6.0 s. By the end of the first 4.0 s both students have reached the same speed of 6.0 m s⁻¹. Which statement about the total distances travelled in the 10 s must be true?
Answer
The correct answer is A.
Correct: A — Student B travels further by about 6 m. A: In 0–4 s, A’s distance is the area of a triangle: 0.5 × 4 × 6 = 12 m; B’s is a trapezium with speeds 3 to 6 m s⁻¹: average 4.5 m s⁻¹ × 4 s = 18 m; both then do 6 s at 6 m s⁻¹ giving 36 m each, so B is ahead by 6 m overall. B: This reverses the conclusion; although A’s acceleration is higher, starting from rest gives less distance in the first 4 s than B’s non-zero start. C: This ignores the first 4 s where B covers an extra 6 m before both move at the same speed. D: This underestimates the difference by halving it; the correct extra distance from B’s higher average speed in the first 4 s is 6 m, not 3 m.