A-LevelMathematicsMechanics9709/42 · Oct/Nov 2024 · Q35 Marks

A cyclist is riding along a straight horizontal road. The total mass of the cyclist and his bicycle is 90kg. The power exerted by the cyclist is 250W. At an instant when the cyclist's speed is 5ms⁻¹, his acceleration is 0.1 ms⁻².

(a)Find the value of the constant resistance to motion acting on the cyclist.[3]
(b)The cyclist comes to the bottom of a hill inclined at 2º to the horizontal. Given that the power and resistance to motion are unchanged, find the steady speed which the cyclist could maintain when riding up the hill.[2]

Mark scheme

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

[B1] For use of power =Fv e.g. 5*PF =250.
[M1] Using their PF≠250.3 terms; allow sign errors. Dimensionally correct.
[A1]
[M1] For attempt at resolving up the hill; 3 terms; allow sign errors; Must be a component of weight (NOT mass) but allow sin/cos mix; allow use of their 41. Dimensionally correct. Oe eg v = 250/(their 41+90g sin 2)
[A1] 3.45258... AWRT 3.45.

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Topic: Mechanics, A-Level Mathematics (syllabus 9709). Structured question, 5 marks.
Source: A-Level Mathematics, Oct/Nov 2024 Paper 4 Variant 2, question 3.

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