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4PM1/01R Jun 2024, Question 6: Motion with Calculus

Pearson Edexcel International GCSE Further Pure Mathematics 4PM1 · Paper 1R · Calculator · 6 marks

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The question, in short

Particle P moves in a straight line with displacement s = e^(2t) sin 3t + 2 metres at t seconds. Points A and B are at t = 0 and t = π/6. Find distance AB and velocity at t = π/3.

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Part (a) · 2 marks

Find the exact distance between points A and B.

  1. 1t = 0: s = e⁰ sin 0 + 2 = 2
  2. 2t = π/6: s = e^(π/3) sin(π/2) + 2 = e^(π/3) + 2
  3. 3AB = e^(π/3)

Answere^(π/3) m

Part (b) · 4 marks

Find the exact velocity of P at t = π/3.

  1. 1v = ds/dt = 2e^(2t) sin 3t + 3e^(2t) cos 3t
  2. 2At t = π/3: sin π = 0 and cos π = −1
  3. 3v = 3e^(2π/3) × (−1) = −3e^(2π/3)

Answer−3e^(2π/3) m/s

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