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4PM1/02 Nov 2023, Question 3: Motion with Calculus

Pearson Edexcel International GCSE Further Pure Mathematics 4PM1 · Paper 2 · Calculator · 7 marks

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The question, in short

Particle P on x-axis has acceleration a = 6t − 16 for t ≥ 0, starts at origin with velocity 12 m/s. Find velocity and displacement expressions, then when P first returns to origin.

Summarised in our own words. Use the official paper for the exact wording and any diagrams.

Part (a) · 4 marks

Find expressions in t for (i) velocity and (ii) displacement of P, using initial position origin and initial velocity 12 m/s.

  1. 1(i) v = ∫(6t − 16) dt = 3t² − 16t + c
  2. 2t = 0, v = 12, so c = 12
  3. 3v = 3t² − 16t + 12
  4. 4(ii) s = ∫(3t² − 16t + 12) dt = t³ − 8t² + 12t + k
  5. 5t = 0, s = 0, so k = 0
  6. 6s = t³ − 8t² + 12t

Answer(i) v = 3t² − 16t + 12; (ii) s = t³ − 8t² + 12t

Part (b) · 3 marks

Using your displacement expression, find the time when P first returns to the origin.

  1. 1s = 0: t³ − 8t² + 12t = 0
  2. 2t(t − 2)(t − 6) = 0
  3. 3t = 0, 2, 6
  4. 4First return: t = 2 s

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