4PM1/02 Nov 2021, Question 6: Motion with Calculus

Pearson Edexcel International GCSE Further Pure Mathematics 4PM1 · Paper 2 · Calculator · 8 marks

The question, in short

A particle P moves on the x-axis with displacement s = t³ − 4t² − 16t − 8 metres at time t seconds (t ≥ 0). Find its initial distance from O, when it is instantaneously at rest, and when its acceleration is 10 m/s² in the positive x direction.

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

Part (a) · 1 mark

Find how far P is from O at t = 0.

1At t = 0, s = −8, so the distance is 8 m

Answer8 m

Part (b) · 4 marks

Find the value of t at which P is instantaneously at rest.

1v = ds/dt = 3t² − 8t − 16
2v = 0: 3t² − 8t − 16 = 0
3(3t + 4)(t − 4) = 0
4t = 4 (t ≥ 0)

Answert = 4

Part (c) · 3 marks

Find the value of t when P has acceleration 10 m/s² in the positive x direction.

1a = d²s/dt² = 6t − 8
26t − 8 = 10
3t = 3

Answert = 3

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