A-LevelMathematicsMechanics9709/41 · May/June 2025 · Q46 Marks

A lorry of mass 18000 kg is travelling along a straight road.

(a)(i)On a horizontal section of the road, the power of the lorry's engine is constant. There is a constant resistance to motion of 1600N. The steady speed which the lorry can maintain with the engine working at power PW is 30ms⁻¹. Find the value of P.[1]
(a)(ii)At an instant when the speed of the lorry is 16 ms⁻¹, its engine is working at a power of 40 kW. Find the acceleration of the lorry at this instant.[2]
(b)When the lorry has reached a speed of 20 ms⁻¹, it begins to ascend a section of road inclined at an angle α° to the horizontal. The engine now works at a power of 120kW. There is no change in the lorry's speed as it ascends the hill. The constant resistance to motion remains 1600N. Find the value of α.[3]

Mark scheme

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

[B1] P/30 - 1600 = 0 ⇒P = 48000 only
[*M1] For use of N2L with 3 dimensionally correct relevant terms. Allow sign errors. (40000/16 - 1600 = 18000a)
[A1] Acceleration = 0.05ms⁻²
[M1] For attempt to resolve up the hill to form an equation. 3 relevant terms, allow sign errors, allow sin/cos mix, allow g missing. (120000/20 - 1600 - 18000g sinα = 0)
[A1]
[A1] α = 1.40 [1.4007...]

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