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Learn/ A Level Mathematics/ Past Papers/ 2023/ Oct/Nov 2023 /Paper 4 (Variant 3)

Mechanics — Variant 3

A Level Mathematics · 9709/43 · Oct/Nov 2023

Question Paper

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Mark Scheme

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Questions

2 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.

3
A block of mass 88 kg slides down a rough plane inclined at 30∘30^\circ to the horizontal, starting from rest. The coefficient of friction between the block and the plane is μ\mu. The block accelerates uniformly down the plane at 2.42.4 m s−2\text{m}\,\text{s}^{-2}.
3(a) [1]
Draw a diagram showing the forces acting on the block.
3(b) [4]
Find the value of μ\mu.
3(c) [1]
Find the speed of the block after it has moved 33 m down the plane.
6
A particle moves in a straight line. At time tt s, the acceleration, aa m s−2\text{m}\,\text{s}^{-2}, of the particle is given by a=36−6ta = 36 - 6t. The velocity of the particle is 2727 m s−1\text{m}\,\text{s}^{-1} when t=2t = 2.
6(a) [4]
Find the values of tt when the particle is at instantaneous rest.
6(b) [4]
Find the total distance the particle travels during the first 1212 seconds.

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