7. A particle \(P\) of mass \(\frac { 1 } { 3 } \mathrm {~kg}\) moves along the positive \(x\)-axis under the action of a single force. The force is directed towards the origin \(O\) and has magnitude \(\frac { k } { ( x + 1 ) ^ { 2 } } \mathrm {~N}\), where \(O P = x\) metres and \(k\) is a constant. Initially \(P\) is moving away from \(O\). At \(x = 1\) the speed of \(P\) is \(4 \mathrm {~m} \mathrm {~s} ^ { - 1 }\), and at \(x = 8\) the speed of \(P\) is \(\sqrt { } 2 \mathrm {~m} \mathrm {~s} ^ { - 1 }\).

1. Find the value of \(k\).
2. Find the distance of \(P\) from \(O\) when \(P\) first comes to instantaneous rest.
   (Total 14 marks)