A-LevelMathematicsMechanics9709/41 · May/June 2017 · Q46 Marks
A car of mass 800 kg is moving up a hill inclined at θ° to the horizontal, where sin θ = 0.15. The initial speed of the car is 8 m s⁻¹. Twelve seconds later the car has travelled 120 m up the hill and has speed 14 m s⁻¹.
- (i)Find the change in the kinetic energy and the change in gravitational potential energy of the car.[3]
- (ii)The engine of the car is working at a constant rate of 32 kW. Find the total work done against the resistive forces during the twelve seconds.[3]
Mark scheme
Marking points from the official mark scheme (May/June 2017). The mark or mark type is shown in brackets.
- KE gain = ½ × 800 × (14² – 8²) = 52800 J
- PE gain = 800 × 10 × 120 × 0.15 = 144000 J
- WD by engine = 32000 × 12
- 32000 x 12 = 144000 + 52800 + WD against F
- WD against F = 187200 J
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