A particle \(P\) moves on the \(x\)-axis. At time \(t\) seconds, \(t \geqslant 0\), the acceleration of \(P\) is
\(( 2 t - 3 ) \mathrm { m } \mathrm { s } ^ { - 2 }\) in the positive \(x\) direction. At time \(t\) seconds, the velocity of \(P\) is \(v \mathrm {~m} \mathrm {~s} ^ { - 1 }\) in the positive \(x\) direction. When \(t = 3 , v = 2\)
Find \(v\) in terms of \(t\).
(4)
The particle first comes to instantaneous rest at the point \(A\) and then comes to instantaneous rest again at the point \(B\).