- At time \(t = 0\) a particle \(P\) leaves the origin \(O\) and moves along the \(x\)-axis. At time \(t\) seconds, the velocity of \(P\) is \(v \mathrm {~m} \mathrm {~s} ^ { - 1 }\) in the positive \(x\) direction, where
$$v = 3 t ^ { 2 } - 16 t + 21$$
The particle is instantaneously at rest when \(t = t _ { 1 }\) and when \(t = t _ { 2 } \left( t _ { 1 } < t _ { 2 } \right)\).
- Find the value of \(t _ { 1 }\) and the value of \(t _ { 2 }\).
- Find the magnitude of the acceleration of \(P\) at the instant when \(t = t _ { 1 }\).
- Find the distance travelled by \(P\) in the interval \(t _ { 1 } \leqslant t \leqslant t _ { 2 }\).
- Show that \(P\) does not return to \(O\).