4MA1/1HR Jan 2022, Question 23: The Second Derivative
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1HR (Higher) · Calculator · 6 marks
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The question, in short
Given displacement functions s = t³ − 4t² + 5t and x = t² − 4t + 4 for t > 1, determine the times when P and Q travel the same way along the line.
Summarised in our own words. Use the official paper for the exact wording and any diagrams.
Solution · 6 marks
- 1Velocity of P: ds/dt = 3t² − 8t + 5 = (3t − 5)(t − 1), zero at t = 5/3
- 2For t > 1, P moves backwards when t < 5/3 and forwards when t > 5/3
- 3Velocity of Q: dx/dt = 2t − 4, backwards when t < 2 and forwards when t > 2
- 4Both move backwards for 1 < t < 5/3 and both forwards for t > 2
- 51 < t < 5/3 and t > 2
Answer1 < t < 5/3 and t > 2
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