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4PM1/02 Jan 2022, Question 5: Motion with Calculus

Pearson Edexcel International GCSE Further Pure Mathematics 4PM1 · Paper 2 · Calculator · 9 marks

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The question, in short

A particle P moves on the x-axis with velocity v = 3t² − 23t + 30 for t ≥ 0. Use this to find rest times, acceleration sign, and a starting coordinate d given positions at t = 0 and t = 8.

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Part (a) · 3 marks

Determine the times t at which the particle's velocity is zero.

  1. 13t² − 23t + 30 = 0
  2. 2(3t − 5)(t − 6) = 0
  3. 3t = 5/3 or t = 6

Answert = 5/3, t = 6

Part (b) · 2 marks

State the interval of t values for which the acceleration is positive.

  1. 1a = dv/dt = 6t − 23
  2. 26t − 23 > 0
  3. 3t > 23/6

Answert > 23/6

Part (c) · 4 marks

Given P starts at (d, 0) and is at (26, 0) when t = 8, calculate d.

  1. 1s = ∫ (3t² − 23t + 30) dt = t³ − 23t²/2 + 30t + c
  2. 2At t = 8: 26 = 512 − 736 + 240 + c
  3. 3c = 10
  4. 4At t = 0: s = c, so d = 10

Answerd = 10

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