The engine of a motorcycle can generate a maximum power of 105kW. The mass of the motorcycle and its rider is 400kg. The total resistance to the motion of the motorcycle and its rider is cvN, where vms⁻¹ is the motorcyclist's speed and c is a constant. The motorcyclist travels along a straight horizontal road under maximum engine power. When the motorcyclist's speed is 35 ms⁻¹, his acceleration is 0.5 ms⁻².

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2025). The mark or mark type is shown in brackets.

1. [1] Driving force F = 105000/35 [=3000] OE e.g. F×35=105000.
2. [1] Use of N2L; allow sign errors but must be 3 terms. Allow F or any non-zero value for the driving force (but not 105000). If assuming a = 0 then e.g. 105000=c×35² (c=85.714...) scores B1 M0.
3. [1] AG a correct equation for c e.g. 3000-35×c=400×0.5 followed by c = 80 scores A1. (2800 = 35c ⇒ c = 80)
4. [1] B1 for correct weight component: ±400g×3/20 or ±400g×sin(sin⁻¹(3/20)). [= ±600].
5. [1] M1 for applying N2L with the correct number of dimensionally correct terms (with a = 0) leading to a three term quadratic equation/expression in v. Allow sign errors and sin/cos mix on the weight component. Must be using c = 80 for this mark.
6. [1] Speed = 32.7 m s⁻¹ ONLY CWO. Allow exact (-15+5√849)/4 or AWRT 32.7. (For reference: 32.6720057...). If negative value (-40.172...) stated, then must be rejected for this mark.