7 A particle \(P\) of mass 0.5 kg moves in a straight line on a smooth horizontal surface. The velocity of \(P\) is \(v \mathrm {~m} \mathrm {~s} ^ { - 1 }\) when the displacement of \(P\) from \(O\) is \(x \mathrm {~m}\). A single horizontal force of magnitude \(0.16 \mathrm { e } ^ { x } \mathrm {~N}\) acts on \(P\) in the direction \(O P\). The velocity of \(P\) when it is at \(O\) is \(0.8 \mathrm {~m} \mathrm {~s} ^ { - 1 }\).

1. Show that \(v = 0.8 \mathrm { e } ^ { \frac { 1 } { 2 } x }\).
2. Find the time taken by \(P\) to travel 1.4 m from \(O\).