A particle \(P\) of mass 0.6 kg is moving along the \(x\)-axis in the positive direction. At time \(t = 0 , P\) passes through the origin \(O\) with speed \(15 \mathrm {~ms} ^ { - 1 }\). At time \(t\) seconds the distance \(O P\) is \(x\) metres, the speed of \(P\) is \(v \mathrm {~m} \mathrm {~s} ^ { - 1 }\) and the resultant force acting on \(P\) has magnitude \(\frac { 12 } { ( t + 2 ) ^ { 2 } }\) newtons. The resultant force is directed towards \(O\).
Show that \(v = 5 \left( \frac { 4 } { t + 2 } + 1 \right)\).