3 At time \(t = 0 \mathrm {~s}\) a particle \(P\), of mass 0.3 kg , is 1 m away from a point \(O\) on a smooth horizontal plane and is moving away from \(O\) with speed \(\sqrt { 5 } \mathrm {~ms} ^ { - 1 }\). The only horizontal force acting on \(P\) has magnitude \(1.5 x \mathrm {~N}\), where \(x\) is the distance \(O P\), and acts away from \(O\).

1. Show that the speed of \(P , v \mathrm {~ms} ^ { - 1 }\), is given by \(v = \sqrt { 5 } x\).
2. Find an expression for \(v\) in terms of \(t\).