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Learn/ A Level Mathematics/ Past Papers/ 2021/ Feb/March 2021 /Paper 4 (Variant 2)

Mechanics — Variant 2

A Level Mathematics · 9709/42 · Feb/March 2021

Question Paper

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Mark Scheme

PDF · 317 KB · 14 pages

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Questions

2 of 7 questions shown here, checked against the paper. The others are in the PDF above — they contain diagrams or maths we could not yet verify, and we would rather show you the original than a transcription we are not sure of.

1 [3]
Two particles PP and QQ of masses 0.20.2 kg and 0.30.3 kg respectively are free to move in a horizontal straight line on a smooth horizontal plane. PP is projected towards QQ with speed 0.50.5 m s−1\text{m s}^{-1}. At the same instant QQ is projected towards PP with speed 11 m s−1\text{m s}^{-1}. QQ comes to rest in the resulting collision. Find the speed of PP after the collision.
6
A particle moves in a straight line. It starts from rest from a fixed point OO on the line. Its velocity at time tt s after leaving OO is vv m s−1\text{m s}^{-1}, where v=t2−8t32+10tv = t^{2} - 8t^{\frac{3}{2}} + 10t.
6(a) [4]
Find the displacement of the particle from OO when t=1t = 1.
6(b) [7]
Show that the minimum velocity of the particle is −125-125 m s−1\text{m s}^{-1}.

Published by Cambridge Assessment International Education. Reproduced for study use.