- A particle \(P\) moves on the \(x\)-axis. At time \(t\) seconds the velocity of \(P\) is \(v \mathrm {~m} \mathrm {~s} ^ { - 1 }\) in the direction of \(x\) increasing, where
$$v = ( t - 2 ) ( 3 t - 10 ) , \quad t \geqslant 0$$
When \(t = 0 , P\) is at the origin \(O\).
- Find the acceleration of \(P\) at time \(t\) seconds.
- Find the total distance travelled by \(P\) in the first 2 seconds of its motion.
- Show that \(P\) never returns to \(O\), explaining your reasoning.