Two particles, A and B, of masses 3 kg and 6 kg respectively, lie on a smooth horizontal plane. Initially, B is at rest and A is moving towards B with speed 8ms⁻¹. After A and B collide, A moves with speed 2ms⁻¹.

Mark scheme

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

1. [*M1] Must have three non-zero terms. Allow sign errors. Must have correct masses with relevant velocities. Their v may be in the opposite direction. If g included with the masses: Allow M1A0A1 for first three marks. Can then score M1M0A0 for final three marks.
2. [A1]
3. [A1] Allow finding only v = 3, but if both speeds found they must both be correct
4. [DM1] Allow use of any v_B even if < 0. Using speed of 5, KE_after = 0.5×3×2^2 + 0.5×6×their 5^2 [=81]. Candidates may work out the loss for each particle separately which only scores DM1 when losses subsequently added together.
5. [DM1] If two speeds found then FT their lower speed, even if later choose the wrong loss. If only one speed found then FT their speed. If the candidate thinks that the particles coalesce then score M0 here
6. [A1] If both losses found, must state which is the greater. Only award this mark if no errors e.g. the KE loss for v=5 should be 15 J. If wrong then A0. Allow -63 [J]. Can score full marks even if only v = 3 is found.