A-LevelMathematicsMechanics9709/43 · Oct/Nov 2019 · Q58 Marks
A cyclist is travelling along a straight horizontal road. The total mass of the cyclist and his bicycle is 80 kg. His power output is a constant 240 W. His acceleration when he is travelling at 6 m s⁻¹ is 0.3 m s⁻².
- (i)Show that the resistance to the cyclist's motion is 16 N.[3]
- (ii)Find the steady speed that the cyclist can maintain if his power output and the resistance force are both unchanged.[2]
- (iii)The cyclist later ascends a straight hill inclined at 3° to the horizontal. His power output and the resistance force are still both unchanged. Find his acceleration when he is travelling at 4 m s⁻¹.[3]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2019). The mark or mark type is shown in brackets.
- [B1] Use of power = force × velocity (Driving force = 240/6 = 40 N)
- [M1] Use of Newton's Second Law (3 terms) (40 - R = 80 × 0.3)
- [A1] AG (Resistance is 16 N)
- [M1] Use of P=Fv with DF=resistance (240/v = 16)
- [A1] Steady speed is 15 ms⁻¹
- [M1] Use of Newton's Second Law (4 terms)
- [A1] (240/4 - 16 - 80g sin3 = 80a)
- [A1] Acceleration is 0.0266 ms⁻²
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