A-LevelMathematicsMechanics9709/43 · May/June 2019 · Q37 Marks
A car of mass 1400kg is travelling up a hill inclined at an angle of 4° to the horizontal. There is a constant resistance to motion of magnitude 1550 N acting on the car.
- (i)Given that the engine of the car is working at 30 kW, find the speed of the car at an instant when its acceleration is 0.4 m s⁻².[4]
- (ii)The greatest possible constant speed at which the car can travel up the hill is 40 m s⁻¹. Find the maximum possible power of the engine.[3]
Mark scheme
Marking points from the official mark scheme (May/June 2019). The mark or mark type is shown in brackets.
- [M1] Use of Newton's Second Law (4 terms): DF-1550-1400gsin4° = 1400 × 0.4
- [A1] (DF = 3086.59...)
- [M1] Use of P = Fv: [30000 = (1400 × 0.4 + 1550 +1400gsin4°)v]
- [A1] v = 9.72 ms⁻¹
- [M1] Resolving up the hill (for constant speed, a=0): (DF = 2526.59...) [DF-1550 – 1400gsin4° = 0]
- [M1] Use of P = Fv: [Pmax = (1550+ 1400gsin4°) × 40]
- [A1] P = 101000 W or 101 kW (P=101063.6...)
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