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4PM1/01 Jun 2024, Question 5: Motion with Calculus

Pearson Edexcel International GCSE Further Pure Mathematics 4PM1 · Paper 1 · Calculator · 9 marks

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The question, in short

A particle P moves on the x-axis with acceleration a = 3t − 4 m/s² for t ≥ 0, starting from rest at t = 0. Work out its velocity, the time T when it is momentarily at rest, and its displacement from the origin at t = 3 given its initial position (−10, 0).

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Part (a) · 3 marks

Determine how fast P is moving at t = 4, using the given acceleration and the fact it starts from rest.

  1. 1v = ∫ (3t − 4) dt = 3t²/2 − 4t + c
  2. 2t = 0, v = 0 gives c = 0
  3. 3v = 3 × 4²/2 − 4 × 4 = 8

Answer8 m/s

Part (b) · 2 marks

Work out the positive time T at which P is momentarily stationary.

  1. 13t²/2 − 4t = 0
  2. 2t(3t/2 − 4) = 0
  3. 3t = 8/3 (t = 0 is the start)

AnswerT = 8/3

Part (c) · 4 marks

Given P begins at (−10, 0), calculate how far it is from the origin at t = 3.

  1. 1x = ∫ (3t²/2 − 4t) dt = t³/2 − 2t² + c
  2. 2t = 0, x = −10 gives c = −10
  3. 3x = 3³/2 − 2 × 3² − 10 = −29/2

Answer−29/2 m

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