6
\includegraphics[max width=\textwidth, alt={}, center]{3e58aa5a-3789-4aaf-8656-b5b98cd7f693-3_518_515_1436_815} Particles \(A\) and \(B\), of masses 0.3 kg and 0.7 kg respectively, are attached to the ends of a light inextensible string. The string passes over a fixed smooth pulley. \(A\) is held at rest and \(B\) hangs freely, with both straight parts of the string vertical and both particles at a height of 0.52 m above the floor (see diagram). \(A\) is released and both particles start to move.

1. Find the tension in the string. When both particles are moving with speed \(1.6 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) the string breaks.
2. Find the time taken, from the instant that the string breaks, for \(A\) to reach the floor.
   \(7 \quad\) A particle \(P\) starts from rest at a point \(O\) and moves in a straight line. \(P\) has acceleration \(0.6 t \mathrm {~m} \mathrm {~s} ^ { - 2 }\) at time \(t\) seconds after leaving \(O\), until \(t = 10\).
3. Find the velocity and displacement from \(O\) of \(P\) when \(t = 10\). After \(t = 10 , P\) has acceleration \(- 0.4 t \mathrm {~m} \mathrm {~s} ^ { - 2 }\) until it comes to rest at a point \(A\).
4. Find the distance \(O A\).