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4PM1/02 Jun 2019, Question 3: Motion with Calculus

Pearson Edexcel International GCSE Further Pure Mathematics 4PM1 · Paper 2 · Calculator · 6 marks

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The question, in short

A particle P travels along a straight line with velocity v = t² − 4t + 7 m/s at time t seconds. Find its acceleration at t = 3 and the distance covered from t = 0 to t = 6.

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Part (a) · 2 marks

Work out how fast the velocity of P is changing, in m/s², at the moment t = 3.

  1. 1dv/dt = 2t − 4
  2. 2t = 3: acceleration = 6 − 4 = 2 m/s²

Answer2 m/s²

Part (b) · 4 marks

Calculate how far P moves, in m, between t = 0 and t = 6.

  1. 1v = (t − 2)² + 3 > 0, so P does not change direction
  2. 2s = ∫ from 0 to 6 of (t² − 4t + 7) dt = [t³/3 − 2t² + 7t] from 0 to 6
  3. 3= 72 − 72 + 42
  4. 4= 42 m

Answer42 m

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