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Learn/ A Level Mathematics/ Past Papers/ 2020/ May/June 2020 /Paper 4 (Variant 3)

Mechanics — Variant 3

A Level Mathematics · 9709/43 · May/June 2020

Question Paper

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Mark Scheme

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Questions

5 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]
Particles PP of mass mm kg and QQ of mass 0.20.2 kg are free to move on a smooth horizontal plane. PP is projected at a speed of 22 m s−1\text{m s}^{-1} towards QQ which is stationary. After the collision PP and QQ move in opposite directions with speeds of 0.50.5 m s−1\text{m s}^{-1} and 11 m s−1\text{m s}^{-1} respectively. Find mm.
2
A minibus of mass 40004000 kg is travelling along a straight horizontal road. The resistance to motion is 900900 N.
2(a) [2]
Find the driving force when the acceleration of the minibus is 0.50.5 m s−2\text{m s}^{-2}.
2(b) [2]
Find the power required for the minibus to maintain a constant speed of 2525 m s−1\text{m s}^{-1}.
4
A car starts from rest and moves in a straight line with constant acceleration aa m s−2\text{m s}^{-2} for a distance of 5050 m. The car then travels with constant velocity for 500500 m for a period of 2525 s, before decelerating to rest. The magnitude of this deceleration is 2a2a m s−2\text{m s}^{-2}.
4(a) [1]
Sketch the velocity-time graph for the motion of the car.
4(b) [3]
Find the value of aa.
4(c) [3]
Find the total time for which the car is in motion.
5
A block BB of mass 44 kg is pushed up a line of greatest slope of a smooth plane inclined at 30∘30^\circ to the horizontal by a force applied to BB, acting in the direction of motion of BB. The block passes through points PP and QQ with speeds 1212 m s−1\text{m s}^{-1} and 88 m s−1\text{m s}^{-1} respectively. PP and QQ are 1010 m apart with PP below the level of QQ.
5(a) [2]
Find the decrease in kinetic energy of the block as it moves from PP to QQ.
5(b) [3]
Hence find the work done by the force pushing the block up the slope as the block moves from PP to QQ.
5(c) [4]
At the instant the block reaches QQ, the force pushing the block up the slope is removed. Find the time taken, after this instant, for the block to return to PP.
6
A particle travels in a straight line PQPQ. The velocity of the particle tt s after leaving PP is vv m s−1\text{m s}^{-1}, where v=4.5+4t−0.5t2v = 4.5 + 4t - 0.5t^{2}.
6(a) [3]
Find the velocity of the particle at the instant when its acceleration is zero. The particle comes to instantaneous rest at QQ.
6(b) [6]
Find the distance PQPQ.

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