3 A particle \(P\) of mass 0.2 kg moves on a smooth horizontal plane. Initially it is projected with velocity \(0.8 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) from a fixed point \(O\) towards another fixed point \(A\). At time \(t\) s after projection, \(P\) is \(x \mathrm {~m}\) from \(O\) and is moving with velocity \(v \mathrm {~m} \mathrm {~s} ^ { - 1 }\), with the direction \(O A\) being positive. A force of \(( 1.5 t - 1 ) \mathrm { N }\) acts on \(P\) in the direction parallel to \(O A\).

1. Find an expression for \(v\) in terms of \(t\).
2. Find the time when the velocity of \(P\) is next \(0.8 \mathrm {~ms} ^ { - 1 }\).
3. Find the times when \(P\) subsequently passes through \(O\).
4. Find the distance \(P\) travels in the third second of its motion.