A particle moves in a straight line, starting from rest at a point O, and comes to instantaneous rest at a point P. The velocity of the particle at time t s after leaving O is v m s⁻¹, where v = 0.6t² – 0.12t³.

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2019). The mark or mark type is shown in brackets.

1. [M1] For attempting to solve v = 0 (0.6t² - 0.12t³ = 0)
2. [A1] (t = 0 or) t = 5
3. [*M1] For integrating the velocity (∫v dt = 0.2t³ - 0.03t⁴)
4. [DM1] Use limits to find OP ([0.2 × 5³ – 0.03 × 5⁴] – [0])
5. [A1] AG (Distance = 6.25 m)
6. [B1] Using s = 6.25 at t = 5 to set up equation in k and c (k × 5³ + c × 5⁵ = 6.25)
7. [*M1] For differentiating s to find v (v = 3kt² + 5ct⁴)
8. [DM1] For using the given value of v = 1.25 in the expression for v (1.25 = 3k × 5² + 5c × 5⁴)
9. [M1] For attempting to solve a pair of simultaneous equations in k and c and finding a value of either k or c (125k + 3125c = 6.25; 75k + 3125c = 1.25)
10. [A1] k = 0.1, c = -0.002
11. [M1] For differentiating their expression for v (a = 0.6t - 0.04t³)
12. [A1] At t = 5, a = -2 (Acceleration = -2 m s⁻²)