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Learn/ A Level Mathematics/ Past Papers/ 2020/ May/June 2020 /Paper 4 (Variant 1)

Mechanics — Variant 1

A Level Mathematics · 9709/41 · May/June 2020

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.

2
A car of mass 18001800 kg is towing a trailer of mass 400400 kg along a straight horizontal road. The car and trailer are connected by a light rigid tow-bar. The car is accelerating at 1.51.5 m s−2\text{m s}^{-2}. There are constant resistance forces of 250250 N on the car and 100100 N on the trailer.
2(a) [2]
Find the tension in the tow-bar.
2(b) [3]
Find the power of the engine of the car at the instant when the speed is 2020 m s−1\text{m s}^{-1}.
3
A particle PP is projected vertically upwards with speed 55 m s−1\text{m s}^{-1} from a point AA which is 2.82.8 m above horizontal ground.
3(a) [3]
Find the greatest height above the ground reached by PP.
3(b) [4]
Find the length of time for which PP is at a height of more than 3.63.6 m above the ground.
6
A particle moves in a straight line ABAB. The velocity vv m s−1\text{m s}^{-1} of the particle tt s after leaving AA is given by v=k(t2−10t+21)v = k(t^{2} - 10t + 21), where kk is a constant. The displacement of the particle from AA, in the direction towards BB, is 2.852.85 m when t=3t = 3 and is 2.42.4 m when t=6t = 6.
6(a) [7]
Find the value of kk. Hence find an expression, in terms of tt, for the displacement of the particle from AA.
6(b) [4]
Find the displacement of the particle from AA when its velocity is a minimum.

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