A car of mass 900 kg is moving on a straight horizontal road ABCD. There is a constant resistance of magnitude 800 N in the sections AB and BC, and a constant resistance of magnitude R N in the section CD. The power of the car's engine is a constant 36 kW.

Mark scheme

Marking points from the official mark scheme (Feb/Mar 2017). The mark or mark type is shown in brackets.

1. [M1] Using P = Fv
2. [A1] Speed of the car v = 45 ms⁻¹
3. [A1] AB = 45 × 120 = 5400 m
4. [M1] Using Newton's 2nd law -800 = 900a [a = −8/9]
5. [M1] Using v² = u² + 2as v² = 45² - (16/9)x450
6. [A1] Speed of the car at C v = 35 ms⁻¹
7. [M1] Attempt change in KE
8. [M1] KE loss = WD against Friction 0.5 × 900 × (45² – v²) = 800 × 450
9. [A1] Speed of the car at C v = 35 ms⁻¹
10. [B1] CD = 6637.5 - 5400-450 = 787.5
11. [M1] Using v² = u² + 2as, a = -d 0 = 35² - 2d x 787.5
12. [A1] d = deceleration d = 7/9 = 0.778 ms⁻²
13. [A1] Using F = ma P = 900 × (7/9) = 700