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Learn/ A Level Mathematics/ Past Papers/ 2020/ May/June 2020 /Paper 4 (Variant 2)

Mechanics — Variant 2

A Level Mathematics · 9709/42 · May/June 2020

Question Paper

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Mark Scheme

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Questions

3 of 6 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
A tram starts from rest and moves with uniform acceleration for 2020 s. The tram then travels at a constant speed, VV m s−1\text{m s}^{-1}, for 170170 s before being brought to rest with a uniform deceleration of magnitude twice that of the acceleration. The total distance travelled by the tram is 2.7752.775 km.
1(a) [2]
Sketch a velocity-time graph for the motion, stating the total time for which the tram is moving.
1(b) [2]
Find VV.
1(c) [2]
Find the magnitude of the acceleration.
5
A car of mass 12501250 kg is moving on a straight road.
5(a)
On a horizontal section of the road, the car has a constant speed of 3232 m s−1\text{m s}^{-1} and there is a constant force of 750750 N resisting the motion.
5(a)(i) [2]
Calculate, in kW, the power developed by the engine of the car.
5(a)(ii) [3]
Given that this power is suddenly decreased by 88 kW, find the instantaneous deceleration of the car.
5(b) [5]
On a section of the road inclined at sin⁡−10.096\sin^{-1} 0.096 to the horizontal, the resistance to the motion of the car is (1000+8v)(1000 + 8v) N when the speed of the car is vv m s−1\text{m s}^{-1}. The car travels up this section of the road at constant speed with the engine working at 6060 kW. Find this constant speed.
6
A particle PP moves in a straight line. The velocity vv m s−1\text{m s}^{-1} at time tt s is given by v=2t+1v = 2t + 1 for 0⩽t⩽50 \leqslant t \leqslant 5, v=36−t2v = 36 - t^{2} for 5⩽t⩽75 \leqslant t \leqslant 7, v=2t−27v = 2t - 27 for 7⩽t⩽13.57 \leqslant t \leqslant 13.5.
6(a) [3]
Sketch the velocity-time graph for 0⩽t⩽13.50 \leqslant t \leqslant 13.5.
6(b) [2]
Find the acceleration at the instant when t=6t = 6.
6(c) [5]
Find the total distance travelled by PP in the interval 0⩽t⩽13.50 \leqslant t \leqslant 13.5.

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