A cyclist is travelling along a straight horizontal road. The total mass of the cyclist and her bicycle is 80 kg. There is a constant resistance force of magnitude 32 N to the cyclist's motion. At an instant when she is travelling at 7ms⁻¹, her acceleration is 0.1 ms⁻².

Mark scheme

Marking points from the official mark scheme (May/June 2024). The mark or mark type is shown in brackets.

1. [B1] For P = DF×7 OE seen at any point in working. Allow any force term or simply DF, e.g. 32,80×0.1, 32-80×0.1, 80×10 etc.
2. [M1] For use of Newton's second law. Must have correct number of terms. Allow sign errors.
3. [A1] 280 W
4. [M1] Attempt at equilibrium equation (a = 0) with their power.
5. [A1FT] Steady speed = 8.75 ms⁻¹ or 35/4 ms⁻¹ [FT their power from part (a) / 32]
6. [B1] Work done by cyclist: 120×4 [480 J]
7. [B1] Kinetic energy terms: 1/2x80v² [40v²] or 1/2x80x7.5² [2250 J] (For at least one KE term.)
8. [B1] Change in PE: 80g×1/20×32.2 [1288 J] [80x10x1.61]
9. [M1] Attempt at work-energy equation with five relevant terms (four relevant terms plus work done against resistance); dimensionally correct. Allow sign errors. Allow sin/cos mix.
10. [A1] 120×4+80g×1/20×32.2-1128 = 1/2x80 (v² -7.5²) [For correct equation.]
11. [A1] Speed = 8.5[0]ms⁻¹ or 17/2 [OE. Use of constant acceleration scores M0 and cannot score B marks if the method leading to their answer only uses constant acceleration.]