A-LevelMathematicsMechanics9709/43 · May/June 2022 · Q58 Marks
A cyclist is riding along a straight horizontal road. The total mass of the cyclist and her bicycle is 70kg. At an instant when the cyclist's speed is 4ms⁻¹, her acceleration is 0.3 ms⁻². There is a constant resistance to motion of magnitude 30N. The cyclist comes to the top of a hill inclined at 5° to the horizontal. The cyclist stops pedalling and freewheels down the hill (so that the cyclist is no longer supplying any power). The magnitude of the resistance force remains at 30N. Over a distance of dm, the speed of the cyclist increases from 6ms⁻¹ to 12 ms⁻¹.
- (a)Find the power developed by the cyclist.[3]
- (b)Find the change in kinetic energy.[2]
- (c)Use an energy method to find d.[3]
Mark scheme
Marking points from the official mark scheme (May/June 2022). The mark or mark type is shown in brackets.
- [M1] Use of Newton's Second law
- [B1] Using P = Fv
- [A1] [= 51 × 4] = 204 W
- [M1] Change in KE = (1/2)×70×12² - (1/2)×70×6²
- [A1] 3780 J
- [M1] For work energy equation
- [A1 FT] 70g × d sin 5 - 30d = 3780 [FT change in kinetic energy from (b)]
- [A1] d = 122
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