A-LevelMathematicsMechanics9709/42 · Oct/Nov 2020 · Q25 Marks
A car of mass 1800 kg is travelling along a straight horizontal road. The power of the car's engine is constant. There is a constant resistance to motion of 650 N.
- (a)Find the power of the car's engine, given that the car's acceleration is 0.5 m s⁻² when its speed is 20 m s⁻¹.[3]
- (b)Find the steady speed which the car can maintain with the engine working at this power.[2]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2020). The mark or mark type is shown in brackets.
- [3] (a) DF - 650 = 1800×0.5 [DF = 1550]
- [3] (a) Apply Newton's second law, 3 terms
- [3] (a) P/20 - 650 = 1800×0.5
- [3] (a) [Power P = 1550 × 20 =] 31 000 W or 31 kW
- [2] (b) 31000/v - 650 = 0
- [2] (b) Use P = Fv with F = 650
- [2] (b) v = 47.7 ms⁻¹
- [2] (b) FT on their P≠ 13 000 Allow 620/13
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