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Learn/ A Level Mathematics/ Past Papers/ 2021/ Oct/Nov 2021 /Paper 4 (Variant 1)

Mechanics — Variant 1

A Level Mathematics · 9709/41 · Oct/Nov 2021

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
A bus moves from rest with constant acceleration for 1212 s. It then moves with constant speed for 3030 s before decelerating uniformly to rest in a further 66 s. The total distance travelled is 585585 m.
1(a) [2]
Find the constant speed of the bus.
1(b) [1]
Find the magnitude of the deceleration.
2
Two small smooth spheres AA and BB, of equal radii and of masses kmkm kg and mm kg respectively, where k>1k > 1, are free to move on a smooth horizontal plane. AA is moving towards BB with speed 66 m s−1\text{m s}^{-1} and BB is moving towards AA with speed 22 m s−1\text{m s}^{-1}. After the collision AA and BB coalesce and move with speed 44 m s−1\text{m s}^{-1}.
2(a) [3]
Find kk.
2(b) [2]
Find, in terms of mm, the loss of kinetic energy due to the collision.
4
A particle of mass 1212 kg is stationary on a rough plane inclined at an angle of 25∘25^\circ to the horizontal. A force of magnitude PP N acting parallel to a line of greatest slope of the plane is used to prevent the particle sliding down the plane. The coefficient of friction between the particle and the plane is 0.350.35.
4(a) [1]
Draw a sketch showing the forces acting on the particle.
4(b) [5]
Find the least possible value of PP.
5
A car of mass 16001600 kg travels at constant speed 2020 m s−1\text{m s}^{-1} up a straight road inclined at an angle of sin⁡−10.12\sin^{-1} 0.12 to the horizontal.
5(a) [3]
Find the change in potential energy of the car in 3030 s.
5(b) [3]
Given that the total work done by the engine of the car in this time is 19601960 kJ, find the constant force resisting the motion.
5(c) [2]
Calculate, in kW, the power developed by the engine of the car.
5(d) [3]
Given that this power is suddenly decreased by 15%15\%, find the instantaneous deceleration of the car.
6
A particle PP moves in a straight line starting from a point OO and comes to rest 1414 s later. At time tt s after leaving OO, the velocity vv m s−1\text{m s}^{-1} of PP is given by v=pt2−qtv = pt^{2} - qt 0⩽t⩽60 \leqslant t \leqslant 6, v=63−4.5tv = 63 - 4.5t 6⩽t⩽146 \leqslant t \leqslant 14, where pp and qq are positive constants. The acceleration of PP is zero when t=2t = 2.
6(a) [3]
Given that there are no instantaneous changes in velocity, find pp and qq.
6(b) [3]
Sketch the velocity-time graph.
6(c) [5]
Find the total distance travelled by PP during the 1414 s.

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