5. A particle \(P\) of mass 0.5 kg moves along the positive \(x\)-axis in the positive \(x\) direction. At time \(t\) seconds, \(t \geqslant 1 , P\) is \(x\) metres from the origin \(O\) and is moving with speed \(v \mathrm {~ms} ^ { - 1 }\). The resultant force acting on \(P\) has magnitude \(\frac { 2 } { x ^ { 3 } } \mathrm {~N}\) and is directed towards \(O\). When \(t = 1 , x = 1\) and \(v = 3\)
Show that

1. \(v ^ { 2 } = \frac { 4 } { x ^ { 2 } } + 5\)
2. \(t = \frac { a + \sqrt { b x ^ { 2 } + c } } { d }\), where \(a , b , c\) and \(d\) are integers to be found.
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