- A particle \(P\) moves along a straight line. At time \(t = 0 , P\) passes the point \(A\) on the line and at time \(t\) seconds the velocity of \(P\) is \(v \mathrm {~m} \mathrm {~s} ^ { - 1 }\) where
$$v = ( 2 t - 3 ) ( t - 2 )$$
At \(t = 3 , P\) reaches the point \(B\). Find the total distance moved by \(P\) as it travels from \(A\) to \(B\).
(6)