2. A particle \(P\) moves along the \(x\)-axis. At time \(t\) seconds its acceleration is \(\left( - 4 \mathrm { e } ^ { - 2 t } \right) \mathrm { m } \mathrm { s } ^ { - 2 }\) in the direction of \(x\) increasing. When \(t = 0 , P\) is at the origin \(O\) and is moving with speed \(1 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) in the direction of \(x\) increasing.

1. Find an expression for the velocity of \(P\) at time \(t\).
2. Find the distance of \(P\) from \(O\) when \(P\) comes to instantaneous rest.
   (6)