4MA1/2H Jan 2022, Question 24: The Second Derivative
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2H (Higher) · Calculator · 5 marks
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The question, in short
Particle P moves on a line through O with displacement x = 4t³ − 27t + 8 metres at time t seconds. Motion reverses at point A; find the acceleration a at A.
Summarised in our own words. Use the official paper for the exact wording and any diagrams.
Solution · 5 marks
- 1Velocity v = dx/dt = 12t² − 27
- 2P changes direction when v = 0, so 12t² − 27 = 0
- 3t² = 27/12 = 9/4, so t = 3/2 (since t ≥ 0)
- 4Acceleration = dv/dt = 24t
- 5a = 24 × 3/2 = 36
Answer36
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