4PM1/02 Jun 2022, Question 2: Motion with Calculus

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

The question, in short

Particle P moves on the x-axis with displacement x = t⁴ − 13.5t + 12 metres at time t seconds. Find its velocity at t = 3, when it is instantaneously at rest, and its acceleration at t = 2.

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

Part (a) · 2 marks

Find the velocity of P in m/s at t = 3.

1v = dx/dt = 4t³ − 13.5
2t = 3: v = 108 − 13.5 = 94.5 m/s

Answer94.5 m/s

Part (b) · 2 marks

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

1At rest: v = 0
24t³ = 13.5 ⇒ t³ = 27/8
3t = 1.5

Answert = 1.5

Part (c) · 2 marks

Find the acceleration of P in m/s² at t = 2.

1a = dv/dt = 12t²
2t = 2: a = 48 m/s²

Answer48 m/s²

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