5. A particle of mass 0.8 kg is moving along the positive \(x\)-axis at a speed of \(5 \mathrm {~ms} ^ { - 1 }\) away from the origin \(O\). When the particle is 2 metres from \(O\) it becomes subject to a single force directed towards \(O\). The magnitude of the force is \(\frac { k } { x ^ { 2 } } \mathrm {~N}\) when the particle is \(x\) metres from \(O\). Given that when the particle is 4 m from \(O\) its speed has been reduced to \(3 \mathrm {~ms} ^ { - 1 }\),

1. show that \(k = \frac { 128 } { 5 }\),
2. find the distance of the particle from \(O\) when it comes to instantaneous rest. (4 marks)