A car of mass 1200 kg has a greatest possible constant speed of 60 m s¯¹ along a straight level road. When the car is travelling at a speed of v m s¯¹ there is a resistive force of magnitude 35v N.

Mark scheme

Marking points from the official mark scheme (Feb/Mar 2018). The mark or mark type is shown in brackets.

1. (i) [M1] Driving force = resistive force at max speed = 35 × 60 = 2100 N
2. (i) [A1] Power = Driving force × speed = 2100 × 60 = 126000 W
3. (ii) [B1FT] Driving force (DF) at v = 30 m s⁻¹ is P/v = 126000 / 30 = 4200 N (FT from previous part for power calculation)
4. (ii) [M1] Newton's 2nd law: DF - Resistive force = ma (4200 - 35 × 30 = 1200a)
5. (ii) [A1] a = 3150 / 1200 = 2.625 m s⁻² AG (Answer Given)
6. (iii) [M1] Driving force DF = P/v = 126000 / v
7. (iii) [M1] For 3-term force equation (constant speed implies a=0): DF = resistive force + component of weight down the plane (126000 / v = 35v + 1200g sin α)
8. (iii) [A1] Correct (unsimplified) equation: 126000 / v = 35v + 1200 × 10 × (7/48)
9. (iii) [M1] Simplify and solve the 3-term quadratic: 35v² + 1750v - 126000 = 0 or v² + 50v - 3600 = 0
10. (iii) [A1] v = 40 m s⁻¹ (reject v = -90 m s⁻¹)