4PM1/02 Jun 2020, Question 1: Motion with Calculus
Pearson Edexcel International GCSE Further Pure Mathematics 4PM1 · Paper 2 · Calculator · 4 marks
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The question, in short
A particle's displacement in metres from a fixed point is s = 3 + 8t + t² − (1/3)t³ for t ≥ 0. Determine how far it is from that point at the moment its velocity is zero.
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Solution · 4 marks
- 1v = ds/dt = 8 + 2t − t²
- 2v = 0: 8 + 2t − t² = (2 + t)(4 − t) = 0
- 3t ≥ 0 ⇒ t = 4
- 4s = 3 + 32 + 16 − 64/3 = 89/3 = 29⅔ m
Answer89/3 m (29⅔ m, or 29.7)
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