A-LevelMathematicsMechanics9709/43 · Oct/Nov 2018 · Q47 Marks

A runner sets off from a point P at time t = 0, where t is in seconds. The runner starts from rest and accelerates at 1.2ms¯² for 5s. For the next 12s the runner moves at constant speed before decelerating uniformly over a period of 3 s, coming to rest at Q. A cyclist sets off from P at time t = 10 and accelerates uniformly for 10s, before immediately decelerating uniformly to rest at Q at time t = 30.

(i)Sketch the velocity-time graph for the runner and show that the distance PQ is 96 m.[4]
(ii)Find the magnitude of the acceleration of the cyclist.[3]

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Mark scheme

Marking points from the official mark scheme (Oct/Nov 2018). The mark or mark type is shown in brackets.

[B1] Three correct straight lines
[B1] Correct trapezium with key values [v = 6 ms¯¹, t = 5 s and t = 17 s]
[M1] Use of trapezium area or use of suvat formulae [½ × 6 × (12+20)] or [½ × 5 × 6 + 12 × 6 + ½ × 3 × 6]
[A1] AG Total distance = 96 m
[M1] Uses area of triangle = 96 or uses s = ut + ½ at² to form equation in a [½ × 20 × v = 96]
[A1] v = 9.6 m s¯¹ or 48 = ½ a (10)²
[A1] Acceleration = 9.6 / 10 = 0.96 m s⁻²

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