2. A particle \(P\) of mass 0.5 kg moves along the positive \(x\)-axis under the action of a single force directed away from the origin \(O\). When \(P\) is \(x\) metres from \(O\), the magnitude of the force is \(3 x ^ { \frac { 1 } { 2 } } \mathrm {~N}\) and \(P\) has a speed of \(v \mathrm {~ms} ^ { - 1 }\). Given that when \(x = 1 , P\) is moving away from \(O\) with speed \(2 \mathrm {~ms} ^ { - 1 }\),

1. find an expression for \(v ^ { 2 }\) in terms of \(x\),
2. show that when \(x = 4 , P\) has a speed of \(7.7 \mathrm {~m} \mathrm {~s} ^ { - 1 }\), correct to 1 decimal place.