A-LevelMathematicsMechanics9709/43 · May/June 2018 · Q69 Marks
A car of mass 1400 kg travelling at a speed of v m s⁻¹ experiences a resistive force of magnitude 40v N. The greatest possible constant speed of the car along a straight level road is 56 m s⁻¹.
- (i)Find, in kW, the greatest possible power of the car's engine.[2]
- (ii)Find the greatest possible acceleration of the car at an instant when its speed on a straight level road is 32 m s⁻¹.[3]
- (iii)The car travels down a hill inclined at an angle of θ° to the horizontal at a constant speed of 50 m s⁻¹. The power of the car's engine is 60 kW. Find the value of θ.[4]
Mark scheme
Marking points from the official mark scheme (May/June 2018). The mark or mark type is shown in brackets.
- [M1] P/56 = 40×56 For equating Power/Velocity to Resistance, or equivalent
- [A1] Power is 125 (kW)
- [B1ft] Driving force is 125440/32 Follow through their power from (i)
- [M1] [125440/32 - 40×32 = 1400a] For 3-term Newton II equation
- [A1] a = 1.89 (m s⁻²)
- [M1] [60000/50 + 1400g sin θ - 40×50 = 0 ] For 3-term Newton II equation
- [A1] [sin θ° = 800/14000] Correct equation
- [M1] θ=3.3
- [A1]
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