A-LevelMathematicsMechanics9709/41 · May/June 2025 · Q37 Marks

The diagram shows the velocity-time graph of the motion of a cyclist. The graph consists of three straight line segments. The cyclist passes a point O with speed 3 ms⁻¹ and then accelerates for 10s with constant acceleration 0.5 ms⁻². He then travels at constant speed for 30s before decelerating, coming to rest at point P, covering a distance of 80m whilst decelerating.

(a)Find the total time taken for the journey from O to P.[3]
(b)On the given axes, sketch a displacement-time graph for the cyclist's journey from O to P, showing on your graph the distances travelled after 10 s and 40 s.[4]

This question uses a diagram from the original paper, which isn't shown here. Open the full paper from the past papers archive to see it.

Mark scheme

Marking points from the official mark scheme (May/June 2025). The mark or mark type is shown in brackets.

[B1] Velocity at t = 10 is 8 [m s⁻¹]
[M1] Attempt to find time for deceleration. Using their 8. (½ × 8(T-40) = 80 OR ½ x 8 x t = 80 [t=20] and T = their t + 40)
[A1] Total time = 60s
[B1FT] FT their 8 15+5v. (Distance after 10s = 55m)
[B1FT] FT their 8 15+35v. (Distance after 40s = 295m)
[B1] For at least one quadratic the right way up or a straight line with positive gradient between t=10 and t=40.
[B1] For fully correct, smooth and continuous at t=10 and t=40. Ignore values on s axis. Ignore curve for t >60 if shown on t-axis.

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