6 A particle \(P\) of mass 2 kg moves along a horizontal straight line. The point \(O\) is a fixed point on this line. At time \(t\) s the velocity of \(P\) is \(v \mathrm {~ms} ^ { - 1 }\) and the displacement of \(P\) from \(O\) is \(x \mathrm {~m}\).
A force of magnitude \(\left( 8 x - \frac { 128 } { x ^ { 3 } } \right) \mathrm { N }\) acts on \(P\) in the direction \(O P\). When \(\mathrm { t } = 0 , \mathrm { x } = 8\) and \(\mathrm { v } = - 15\).

1. Show that \(\mathrm { v } = - \frac { 2 } { \mathrm { x } } \left( \mathrm { x } ^ { 2 } - 4 \right)\).
2. Find an expression for \(x\) in terms of \(t\).