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4PM1/01R Jun 2025, Question 3: Motion with Calculus

Pearson Edexcel International GCSE Further Pure Mathematics 4PM1 · Paper 1R · Calculator · 10 marks

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The question, in short

Particle P moves on a line from origin O with velocity v = 2t² − 19t + 35 m/s at time t ≥ 0. Use this to find when acceleration is zero, when P is at rest, and the distance travelled between those rest times.

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

Part (a) · 3 marks

Find the time t at which the acceleration a of P equals 0.

  1. 1a = dv/dt = 4t − 19
  2. 24t − 19 = 0
  3. 3t = 19/4

Answert = 19/4

Part (b) · 3 marks

Find the two times T₁ and T₂ (T₂ > T₁) when P is instantaneously at rest.

  1. 1v = 0: 2t² − 19t + 35 = 0
  2. 2(2t − 5)(t − 7) = 0
  3. 3T₁ = 5/2, T₂ = 7

AnswerT₁ = 5/2, T₂ = 7

Part (c) · 4 marks

Find the exact distance in metres P travels between times T₁ and T₂, showing working.

  1. 1∫ (2t² − 19t + 35) dt = (2/3)t³ − (19/2)t² + 35t
  2. 2Evaluate from t = 5/2 to t = 7: 49/6 − 925/24 = −243/8
  3. 3Distance is positive: 243/8 m

Answer243/8 m

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