A particle A moves in a straight line with constant speed 10 m s⁻¹. Two seconds after A passes a point O on the line, a particle B passes through O, moving along the line in the same direction as A. Particle B has speed 16 m s⁻¹ at O and has a constant deceleration of 2 m s⁻².

Mark scheme

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

1. M1 Attempt s_A as s_A = k + 10t (any k)
2. A1 s_A = 20 + 10t
3. B1 FT Allow FT only if s_A = 10t and s_B = 16(t − 2) + ½(−2)(t − 2)² i.e. t measured from when A passes O
4. B1 v_B = 16 - 2t → v_B = 0, t = 8
5. M1 Finding distance between A and B at time t = T (T > 0) found from a valid method for v_B = 0
6. A1 t = 8, s = 36 (m)
7. M1 Either use differentiation or complete the square, or state value of t when speeds are the same
8. M1 Solve for t and evaluate s_A – s_B at this value of t
9. A1 s = s_A-s_B = 11 m