1. A particle \(P\) of mass \(m \mathrm {~kg}\) is initially held at rest at the point \(O\) on a smooth inclined plane. The plane is inclined at an angle \(\alpha\) to the horizontal, where \(\sin \alpha = \frac { 2 } { 5 }\)

The particle is released from rest and slides down the plane against a force which acts towards \(O\). The force has magnitude \(\frac { 1 } { 3 } m x ^ { 2 } \mathrm {~N}\), where \(x\) metres is the distance of \(P\) from \(O\).

1. Find the speed of \(P\) when \(x = 2\) The particle first comes to instantaneous rest at the point \(A\).
2. Find the distance \(O A\).