A-LevelMathematicsMechanics9709/42 · May/June 2024 · Q47 Marks

A car has mass 1400kg. When the speed of the car is vms⁻¹ the magnitude of the resistance to motion is kv²N where k is a constant.

(a)(i)Find the value of k.[1]
(a)(ii)Find the power of the car's engine.[3]
(b)The car now moves at a constant speed on a straight level road. Given that its engine is working at 54kW, find this speed.[3]

Mark scheme

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

[B1] OE, e.g. 480/576, 0.833 or better.
[M1] 3 terms; allow sign errors; allow sin/cos mix.
[DB1] For using P = DF x v, where DF is numerical.
[A1] Allow W missing, but if given in kW units must be present. Allow 51.84kW. Allow 51800, 51.8kW.
[B1FT] FT their k > 0.
[DM1] a and b must both be positive or both negative. Must get to a value for v; if cubic not seen, the cubic may be implied by the correct answer for their equation.
[A1] 40.165977. AWRT 40.2 from correct work.

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Topic: Mechanics, A-Level Mathematics (syllabus 9709). Structured question, 7 marks.
Source: A-Level Mathematics, May/June 2024 Paper 4 Variant 2, question 4.

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