6 A particle \(P\) of mass 0.5 kg moves in a straight line on a smooth horizontal surface. At time \(t \mathrm {~s}\), the displacement of \(P\) from a fixed point on the line is \(x \mathrm {~m}\) and the velocity of \(P\) is \(v \mathrm {~m} \mathrm {~s} ^ { - 1 }\). It is given that when \(t = 0 , x = 0\) and \(v = 9\). The motion of \(P\) is opposed by a force of magnitude \(3 \sqrt { } v \mathrm {~N}\).

1. By solving an appropriate differential equation, show that \(v = ( 27 - 9 x ) ^ { \frac { 2 } { 3 } }\).
2. Calculate the value of \(x\) when \(t = 0.5\).