5 A particle \(P\) of mass 0.4 kg is released from rest at a point \(O\) on a smooth plane inclined at \(30 ^ { \circ }\) to the horizontal. A force of magnitude \(3 \mathrm { e } ^ { - t } \mathrm {~N}\) directed up a line of greatest slope acts on \(P\), where \(t \mathrm {~s}\) is the time after release.

1. Show that \(\frac { \mathrm { d } v } { \mathrm {~d} t } = 7.5 \mathrm { e } ^ { - t } - 5\), where \(v \mathrm {~m} \mathrm {~s} ^ { - 1 }\) is the velocity of \(P\) up the plane at time \(t \mathrm {~s}\).
2. Express \(v\) in terms of \(t\).
3. Find the distance of \(P\) from \(O\) when \(v\) has its maximum value.