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AS Daily A Level Physics question

2025-09-19 OCR A Kinematics (velocity–time, acceleration), Basic algebra 3.1.1(d)

A trolley on a straight track starts from rest. Trial 1: it reaches 8.0 m/s uniformly in 4.0 s, then continues at 8.0 m/s for a further 2.0 s. Trial 2: it reaches the same 8.0 m/s uniformly in 2.0 s, then continues at 8.0 m/s so the total time is still 6.0 s. Ignore resistive forces. Which statement must be true about the total displacement over the 6.0 s?

  1. A The displacements are equal because the final speed is the same in both trials.
  2. B Trial 1 gives greater displacement because it accelerates for longer.
  3. C Trial 2 gives smaller displacement because the average acceleration is larger.
  4. D Trial 2 gives greater displacement by 8 m because it spends more time at 8 m/s. (correct)

Answer

The correct answer is D.

Correct: D — Trial 2 gives greater displacement by 8 m because it spends more time at 8 m/s. A The same final speed does not guarantee the same displacement; the area under the velocity–time graph differs. B Longer acceleration time does not necessarily increase displacement; Trial 1’s areas are 0.5×4×8 = 16 m (accelerating) and 8×2 = 16 m (constant) for 32 m total, less than Trial 2. C A larger average acceleration does not reduce displacement here; reaching top speed earlier increases the area under the curve. D In Trial 2 the areas are 0.5×2×8 = 8 m and 8×4 = 32 m for 40 m total, which is 8 m greater.

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