A car travels along a straight road with constant acceleration a ms⁻², where a > 0. The car passes through points A, B and C in that order. The speed of the car at A is u ms⁻¹ in the direction AB. The distance BC is twice the distance AB. The car takes 8 seconds to travel from A to B and 10 seconds to travel from B to C.

Mark scheme

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

1. [B1B1] For use of `s = ut + 1/2 at^2` or `s = (u+v)/2 * t`. B1 for any one correct expression, B2 for two correct expressions.
2. [M1] To obtain an equation in u and a only. Must have come from correct expressions but allow x 1/3 instead of x3 or x 1/2 instead of x2 or x 2/3 instead of x3/2.
3. [A1] u = 11a
4. [M1] For use of `v=u+at` or other complete suvat method. Using their u in terms of a, e.g. `v² = (11a)² + 2a(18×11a+162a) [=841a²]`, `v = √(11a)² +2a(18×11a+162a) [= √841a²]`.
5. [A1FT] FT their expression for v so their u + 18a.