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Learn/ A Level Mathematics/ Past Papers/ 2022/ May/June 2022 /Paper 4 (Variant 3)

Mechanics — Variant 3

A Level Mathematics · 9709/43 · May/June 2022

Question Paper

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Mark Scheme

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Questions

3 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
Two particles PP and QQ, of masses 0.30.3 kg and 0.20.2 kg respectively, are at rest on a smooth horizontal plane. PP is projected at a speed of 44 m s−1\text{m s}^{-1} directly towards QQ. After PP and QQ collide, QQ begins to move with a speed of 33 m s−1\text{m s}^{-1}.
1(a) [2]
Find the speed of PP after the collision. After the collision, QQ moves directly towards a third particle RR, of mass mm kg, which is at rest on the plane. The two particles QQ and RR coalesce on impact and move with a speed of 22 m s−1\text{m s}^{-1}.
1(b) [2]
Find mm.
2
A particle PP is projected vertically upwards from horizontal ground. PP reaches a maximum height of 4545 m. After reaching the ground, PP comes to rest without rebounding.
2(a) [2]
Find the speed at which PP was projected.
2(b) [3]
Find the total time for which the speed of PP is at least 1010 m s−1\text{m s}^{-1}.
7
A particle PP moves in a straight line through a point OO. The velocity vv m s−1\text{m s}^{-1} of PP, at time tt s after passing OO, is given by v=94+b(t+1)2−ct2v = \frac{9}{4} + \frac{b}{(t + 1)^{2}} - ct^{2}, where bb and cc are positive constants. At t=5t = 5, the velocity of PP is zero and its acceleration is −1312-\frac{13}{12} m s−2\text{m s}^{-2}.
7(a) [5]
Show that b=9b = 9 and find the value of cc.
7(b) [5]
Given that the velocity of PP is zero only at t=5t = 5, find the distance travelled in the first 1010 seconds of motion.

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