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Learn/ A Level Mathematics/ Past Papers/ 2023/ Feb/March 2023 /Paper 4 (Variant 2)

Mechanics — Variant 2

A Level Mathematics · 9709/42 · Feb/March 2023

Question Paper

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Mark Scheme

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Questions

4 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 crate of mass 200200 kg is being pulled at constant speed along horizontal ground by a horizontal rope attached to a winch. The winch is working at a constant rate of 4.54.5 kW and there is a constant resistance to the motion of the crate of magnitude 600600 N.
1(a) [2]
Find the time that it takes for the crate to move a distance of 1515 m. The rope breaks after the crate has moved 1515 m.
1(b) [3]
Find the time taken, after the rope breaks, for the crate to come to rest.
2
A particle PP is projected vertically upwards from horizontal ground with speed 1515 m s−1\text{m s}^{-1}.
2(a) [2]
Find the speed of PP when it is 1010 m above the ground. At the same instant that PP is projected, a second particle QQ is dropped from a height of 1818 m above the ground in the same vertical line as PP.
2(b) [3]
Find the height above the ground at which the two particles collide.
3
A particle moves in a straight line starting from rest from a point OO. The acceleration of the particle at time tt s after leaving OO is aa m s−2\text{m s}^{-2}, where a=4t12a = 4t^{\frac{1}{2}}.
3(a) [2]
Find the speed of the particle when t=9t = 9.
3(b) [3]
Find the time after leaving OO at which the speed (in metres per second) and the distance travelled (in metres) are numerically equal.
4
A toy railway locomotive of mass 0.80.8 kg is towing a truck of mass 0.40.4 kg on a straight horizontal track at a constant speed of 22 m s−1\text{m s}^{-1}. There is a constant resistance force of magnitude 0.20.2 N on the locomotive, but no resistance force on the truck. There is a light rigid horizontal coupling connecting the locomotive and the truck.
4(a) [1]
State the tension in the coupling.
4(b) [1]
Find the power produced by the locomotive's engine. The power produced by the locomotive's engine is now changed to 1.21.2 W.
4(c) [5]
Find the magnitude of the tension in the coupling at the instant that the locomotive begins to accelerate.

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