A-LevelMathematicsMechanics9709/42 · Feb/Mar 2021 · Q26 Marks

A car of mass 1400 kg is travelling at constant speed up a straight hill inclined at α to the horizontal, where sin α = 0.1. There is a constant resistance force of magnitude 600 N. The power of the car's engine is 22 500 W.

(a)Show that the speed of the car is 11.25 ms¯¹.[3]
(b)The car, moving with speed 11.25 m s¯¹, comes to a section of the hill which is inclined at 2° to the horizontal. Given that the power and resistance force do not change, find the initial acceleration of the car up this section of the hill.[3]

Mark scheme

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

[1] Driving force = DF = 22500 / v
[1] Apply Newton's 2nd law to the car with a = 0, three relevant terms. May see term 1400g sin 5.7° .
[1] AG From exact working only, may be implied if using 5.7° .
[1] Use of Newton's second law for the car, 4 relevant terms.
[1]
[1]

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Topic: Mechanics, A-Level Mathematics (syllabus 9709). Structured question, 6 marks.
Source: A-Level Mathematics, Feb/Mar 2021 Paper 4 Variant 2, question 2.

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