6 A particle \(P\) of mass 2 kg moving on a horizontal straight line has displacement \(x \mathrm {~m}\) from a fixed point \(O\) on the line and velocity \(v \mathrm {~m} \mathrm {~s} ^ { - 1 }\) at time \(t \mathrm {~s}\). The only horizontal force acting on \(P\) has magnitude \(\frac { 1 } { 10 } ( 2 \mathrm { v } - 1 ) ^ { 2 } \mathrm { e } ^ { - \mathrm { t } } \mathrm { N }\) and acts towards \(O\). When \(t = 0 , x = 1\) and \(v = 3\).

1. Find an expression for \(v\) in terms of \(t\).
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2. Find an expression for \(x\) in terms of \(t\).