4 A particle \(P\) moves in a straight line. It starts from rest at a point \(O\) on the line and at time \(t \mathrm {~s}\) after leaving \(O\) it has acceleration \(a \mathrm {~m} \mathrm {~s} ^ { - 2 }\), where \(a = 6 t - 18\). Find the distance \(P\) moves before it comes to instantaneous rest.
\includegraphics[max width=\textwidth, alt={}, center]{de5edcfa-595b-4a9b-b3b3-7803670759cf-06_540_606_258_767} Two particles of masses 0.8 kg and 0.2 kg are connected by a light inextensible string that passes over a fixed smooth pulley. The system is released from rest with both particles 0.5 m above a horizontal floor (see diagram). In the subsequent motion the 0.2 kg particle does not reach the pulley.

1. Show that the magnitude of the acceleration of the particles is \(6 \mathrm {~m} \mathrm {~s} ^ { - 2 }\) and find the tension in the string.
2. When the 0.8 kg particle reaches the floor it comes to rest. Find the greatest height of the 0.2 kg particle above the floor.