5. A particle \(P\) of mass 0.4 kg moves on the positive \(x\)-axis under the action of a single force. The force is directed towards the origin \(O\) and has magnitude \(\frac { k } { x ^ { 2 } }\) newtons, where \(O P = x\) metres and \(k\) is a constant. Initially \(P\) is moving away from \(O\). At \(x = 2\) the speed of \(P\) is \(5 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) and at \(x = 5\) the speed of \(P\) is \(2 \mathrm {~m} \mathrm {~s} ^ { - 1 }\).
- Find the value of \(k\).
The particle first comes to instantaneous rest at the point \(A\).
- Find the value of \(x\) at \(A\).