7 A particle \(P\) of mass 0.2 kg is released from rest at a point \(O\) on a rough plane inclined at \(60 ^ { \circ }\) to the horizontal, and travels down a line of greatest slope. The coefficient of friction between \(P\) and the plane is 0.3 . A force of magnitude \(0.6 x \mathrm {~N}\) acts on \(P\) in the direction \(P O\), where \(x \mathrm {~m}\) is the displacement of \(P\) from \(O\).

1. Show that \(v \frac { \mathrm {~d} v } { \mathrm {~d} x } = 5 \sqrt { } 3 - 1.5 - 3 x\), where \(v \mathrm {~m} \mathrm {~s} ^ { - 1 }\) is the velocity of \(P\) at a displacement \(x \mathrm {~m}\) from \(O\).
2. Find the value of \(x\) for which \(P\) reaches its maximum velocity, and calculate this maximum velocity.
3. Calculate the magnitude of the acceleration of \(P\) immediately after it has first come to instantaneous rest.