A-LevelMathematicsMechanics9709/42 · May/June 2017 · Q49 Marks
A car of mass 1200 kg is moving on a straight road against a constant force of 850 N resisting the motion.
- (i)(a)On a part of the road that is horizontal, the car moves with a constant speed of 42 m s⁻¹. Calculate, in kW, the power developed by the engine of the car.[2]
- (b)Given that this power is suddenly increased by 6 kW, find the instantaneous acceleration of the car.[3]
- (ii)On a part of the road that is inclined at θ° to the horizontal, the car moves up the hill at a constant speed of 24 m s⁻¹, with the engine working at 80 kW. Find θ.[4]
Mark scheme
Marking points from the official mark scheme (May/June 2017). The mark or mark type is shown in brackets.
- M1 Using P = Fv
- A1 Must be in kW to 3sf
- M1 Find new power and new DF based on power found in 4(i)(a)
- M1 Apply Newton 2, three terms
- A1 a = 5/42 = 0.119 ms⁻²
- B1 DF = P/v
- M1 Newton 2 along the hill, 3 terms
- M1 Solve for θ, from a three term equation
- A1 θ = 11.9
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