O-LevelAdditional MathematicsDifferentiation and integration4037/11 · May/June 2021 · Q710 Marks

(a) In this question, all lengths are in metres and time, t, is in seconds. [Figure 7.1] The diagram shows the displacement-time graph for a runner, for 0 ≤ t ≤ 40. (b) A particle, P, moves in a straight line such that its displacement from a fixed point at time t is s. The acceleration of P is given by (2t+4)^(-1/2), for t > 0.

(a)(i)Find the distance the runner has travelled when t = 40.[1]
(a)(ii)On the axes, draw the corresponding velocity-time graph for the runner, for 0 ≤ t ≤ 40.[2]
(b)(i)Given that P has a velocity of 9 when t = 6, find the velocity of P at time t.[3]
(b)(ii)Given that s = 1/3 when t = 6, find the displacement of P at time t.[3]

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Mark scheme

Marking points from the official mark scheme (May/June 2021). The mark or mark type is shown in brackets.

[1] B1
[2] B2 B1 for a line joining (0,5) and (10,5) B1 for a line joining (10,-2) and (40,-2)
[3] M1 For k(2t+4)2
[3] M1 Dep for attempt to find c using v = 9 and t = 6 in their v
[3] A1
[3] M1 For k(2t+4)2
[3] M1 Dep for attempt to find d using s = 1/3 and t = 6 in their s
[3] A1

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