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Learn/ A Level Mathematics/ Past Papers/ 2020/ Oct/Nov 2020 /Paper 4 (Variant 2)

Mechanics — Variant 2

A Level Mathematics · 9709/42 · Oct/Nov 2020

Question Paper

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Mark Scheme

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Questions

4 of 8 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 0.20.2 kg and 0.50.5 kg respectively, are at rest on a smooth horizontal plane. PP is projected towards QQ with speed 22 m s−1\text{m s}^{-1}.
1(a) [1]
Write down the momentum of PP.
1(b) [2]
After the collision PP continues to move in the same direction with speed 0.30.3 m s−1\text{m s}^{-1}. Find the speed of QQ after the collision.
2
A car of mass 18001800 kg is travelling along a straight horizontal road. The power of the car's engine is constant. There is a constant resistance to motion of 650650 N.
2(a) [3]
Find the power of the car's engine, given that the car's acceleration is 0.50.5 m s−2\text{m s}^{-2} when its speed is 2020 m s−1\text{m s}^{-1}.
2(b) [2]
Find the steady speed which the car can maintain with the engine working at this power.
5
A particle is projected vertically upwards with speed 4040 m s−1\text{m s}^{-1} alongside a building of height hh m.
5(a) [4]
Given that the particle is above the level of the top of the building for 44 s, find hh.
5(b) [4]
One second after the first particle is projected, a second particle is projected vertically upwards from the top of the building with speed 2020 m s−1\text{m s}^{-1}. Denoting the time after projection of the first particle by tt s, find the value of tt for which the two particles are at the same height above the ground.
7
A particle PP moves in a straight line, starting from a point OO with velocity 1.721.72 m s−1\text{m s}^{-1}. The acceleration aa m s−2\text{m s}^{-2} of the particle, tt s after leaving OO, is given by a=0.1t32a = 0.1t^{\frac{3}{2}}.
7(a) [4]
Find the value of tt when the velocity of PP is 33 m s−1\text{m s}^{-1}.
7(b) [3]
Find the displacement of PP from OO when t=2t = 2, giving your answer correct to 2 decimal places.

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