4PM1/01R Jun 2022, Question 2: Motion with Calculus
Pearson Edexcel International GCSE Further Pure Mathematics 4PM1 · Paper 1R · Calculator · 7 marks
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The question, in short
Particle P moves on a line through fixed point O with velocity v = t² − 3t + 4 m/s at time t seconds. Use this to find acceleration and displacement.
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Part (a) · 2 marks
Find an expression for the acceleration a in terms of t.
- 1a = dv/dt = 2t − 3
Answera = 2t − 3
Part (b) · 5 marks
Given displacement from O is 7 m at t = 2, find the exact displacement from O at t = 4.
- 1s = ∫ (t² − 3t + 4) dt = t³/3 − (3/2)t² + 4t + C
- 2t = 2, s = 7: 8/3 − 6 + 8 + C = 7 ⇒ C = 7/3
- 3t = 4: s = 64/3 − 24 + 16 + 7/3
- 4s = 47/3 m
Answer47/3 m
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