2. A particle \(P\) moves along the \(x\)-axis. At time \(t\) seconds the velocity of \(P\) is \(v \mathrm {~m} \mathrm {~s} ^ { - 1 }\) and its acceleration is \(2 \sin \frac { 1 } { 2 } t \mathrm {~m} \mathrm {~s} ^ { - 2 }\), both measured in the direction of \(O x\). Given that \(v = 4\) when \(t = 0\),

1. find \(v\) in terms of \(t\),
2. calculate the distance travelled by \(P\) between the times \(t = 0\) and \(t = \frac { \pi } { 2 }\).