- A particle \(P\) of mass 0.5 kg moves on the positive \(x\)-axis under the action of a single force directed towards the origin \(O\). At time \(t\) seconds the distance of \(P\) from \(O\) is \(x\) metres, the magnitude of the force is \(0.375 x ^ { 2 } \mathrm {~N}\) and the speed of \(P\) is \(v \mathrm {~m} \mathrm {~s} ^ { - 1 }\).
When \(t = 0 , O P = 8 \mathrm {~m}\) and \(P\) is moving towards \(O\) with speed \(2 \mathrm {~m} \mathrm {~s} ^ { - 1 }\).
- Show that \(v ^ { 2 } = 260 - \frac { 1 } { 2 } \chi ^ { 3 }\).
- Find the distance of \(P\) from \(O\) at the instant when \(v = 5\).