A-LevelMathematicsMechanics9709/41 · Oct/Nov 2024 · Q46 Marks

A bus travels between two stops, A and B. The bus starts from rest at A and accelerates at a constant rate of a ms⁻² until it reaches a speed of 16 ms⁻¹. It then travels at this constant speed before decelerating at a constant rate of 0.75a ms⁻², coming to rest at B. The total time for the journey is 240 s.

(a)Sketch the velocity-time graph for the bus’s journey from A to B.[1]
(b)Find an expression, in terms of a, for the length of time that the bus is travelling with constant speed.[2]
(c)Given that the distance from A to B is 3000m, find the value of a.[3]

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Mark scheme

Marking points from the official mark scheme (Oct/Nov 2024). The mark or mark type is shown in brackets.

B1 Correct shape, starting at O and finishing on the t-axis.
*B1 t_1 = 16/a, t_3 = 64/(3a)
DB1 T = 240 - (16/a + 64/(3a))
*M1 3000 = (1/2) × 16 × (240 + (240 - (16/a + 64/(3a))))
DM1 Get an expression in terms of a ONLY using their T from part (b) and solve for a – their T must have come from an expression of the form 240 - k₁/a - k₂/a where k₁ and k₂ are positive constants.
A1 a = 16/45

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