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4PM1/02R Jun 2023, Question 5: Motion with Calculus

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

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The question, in short

Particle P moves on the x-axis with velocity v = 2t² − 19t + 35 for t ≥ 0. Find acceleration at t = 5, the two rest times, and the distance AB using calculus.

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

Part (a) · 2 marks

Find the acceleration of P at t = 5 from the given velocity expression.

  1. 1a = dv/dt = 4t − 19
  2. 2When t = 5: a = 20 − 19 = 1 m/s²

Answer1 m/s²

Part (b) · 2 marks

Find the two times t₁ and t₂, with t₁ < t₂, when P is instantaneously at rest.

  1. 12t² − 19t + 35 = 0
  2. 2(2t − 5)(t − 7) = 0
  3. 3t₁ = 5/2, t₂ = 7

Answert₁ = 5/2, t₂ = 7

Part (c) · 3 marks

Use calculus to find the distance between points A and B.

  1. 1∫ from 5/2 to 7 of (2t² − 19t + 35) dt = [2t³/3 − 19t²/2 + 35t] from 5/2 to 7
  2. 2= 49/6 − 925/24 = −243/8
  3. 3Distance AB = 243/8 m (= 30.375 m)

Answer243/8 m

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