A-LevelMathematicsMechanics9709/42 · Feb/Mar 2023 · Q35 Marks

A particle moves in a straight line starting from rest from a point O. The acceleration of the particle at time t s after leaving O is a m s⁻², where a = 4t^(1/2).

(a)Find the speed of the particle when t = 9.[2]
(b)Find the time after leaving O at which the speed (in metres per second) and the distance travelled (in metres) are numerically equal.[3]

Mark scheme

Marking points from the official mark scheme (Feb/Mar 2023). The mark or mark type is shown in brackets.

[M1] Attempt to integrate v = ∫a dt. Increasing power by 1 and a change in coefficient in at least one term; may be unsimplified.
[A1] Substitute t=9 to get speed = 72ms⁻¹ Or use limits t = 0 and t=9.
[*M1] Attempt at integration of their v. Increasing power by 1 and a change in coefficient in at least one term; may be unsimplified. Their v, which has come from integration in part (a).
[DM1] Equate their v and their s and attempt to solve for t. Their v must have come from integration. Allow if their c from (a) is not 0.
[A1] time = 5/2 s Must discard t=0 and t = -5/2

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Topic: Mechanics, A-Level Mathematics (syllabus 9709). Structured question, 5 marks.
Source: A-Level Mathematics, Feb/Mar 2023 Paper 4 Variant 2, question 3.

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