A-LevelMathematicsMechanics9709/41 · Oct/Nov 2018 · Q610 Marks

A particle is projected from a point P with initial speed u m s⁻¹ up a line of greatest slope PQR of a rough inclined plane. The distances PQ and QR are both equal to 0.8 m. The particle takes 0.6 s to travel from P to Q and 1 s to travel from Q to R.

(i)Show that the deceleration of the particle is 2/3 m s⁻² and hence find u, giving your answer as an exact fraction.[6]
(ii)Given that the plane is inclined at 3° to the horizontal, find the value of the coefficient of friction between the particle and the plane.[4]

Mark scheme

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

[M1] For using constant acceleration equations such as s = ut + 1/2 at² or equivalent complete methods to find expressions for PQ or QR or PR
[A1] For PQ 0.8 = 0.6u + 0.18a
[A1] For PR 1.6 = 1.6u + 1.28a or for QR 0.8 = (u + a × 0.6) × 1 + 0.5a
[M1] Solving simultaneously two relevant equations in u and a
[A1] AG
[B1] u = 23/15
[B1] R = mg cos 3
[M1] For use of F = μR
[M1] For using Newton's second law (3 terms)
[A1] μ = 0.0144 (0.014350...)

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