A particle \(P\) moves on the \(x\)-axis. The acceleration of \(P\), in the positive \(x\) direction at time \(t\) seconds, is \(( 2 t - 3 ) \mathrm { m } \mathrm { s } ^ { - 2 }\). The velocity of \(P\), in the positive \(x\) direction at time \(t\) seconds, is \(v \mathrm {~m} \mathrm {~s} ^ { - 1 }\). When \(t = 0 , v = 2\)
Find \(v\) in terms of \(t\).
The particle is instantaneously at rest at times \(t _ { 1 }\) seconds and \(t _ { 2 }\) seconds, where \(t _ { 1 } < t _ { 2 }\).
Find the values \(t _ { 1 }\) and \(t _ { 2 }\).
Find the distance travelled by \(P\) between \(t = t _ { 1 }\) and \(t = t _ { 2 }\).