A particle \(P\) of mass \(m \mathrm {~kg}\) is initially held at rest at the point \(O\) on a smooth plane which is inclined at \(30 ^ { \circ }\) to the horizontal. The particle is released from rest and slides down the plane against a force of magnitude \(\frac { 1 } { 2 } m x ^ { 2 }\) newtons acting towards \(O\), where \(x\) metres is the distance of \(P\) from \(O\).
Find the speed of \(P\) when \(x = 3\)
Find the distance \(P\) has moved when it first comes to instantaneous rest.