4MA1/2H Jan 2021, Question 19: Stationary Points and Turning Points
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2H (Higher) · Calculator · 5 marks
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The question, in short
A particle P moves on a line through fixed point O, with displacement s = t³ + 5t² − 8t + 10 metres at time t ≥ 0 seconds. Find P's displacement from O at the instant P is at rest, giving it as a/b.
Summarised in our own words. Use the official paper for the exact wording and any diagrams.
Solution · 5 marks
- 13t² + 10t − 8
- 23t² + 10t − 8 = 0
- 3(3t − 2)(t + 4) = 0
- 4t = 2/3 or t = −4
- 5t = 2/3 (since t ≥ 0)
- 6s = (2/3)³ + 5(2/3)² − 8(2/3) + 10
- 7s = 8/27 + 20/9 − 16/3 + 10
- 8s = 8/27 + 60/27 − 144/27 + 270/27
- 9s = (8 + 60 − 144 + 270)/27
- 10s = 194/27
Answer194/27
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