- A particle \(P\) moves along a straight line. The fixed point \(O\) is on the line. At time \(t\) seconds, \(t > 0\), the displacement of \(P\) from \(O\) is \(x\) metres, where
$$x = 2 t ^ { 3 } - 21 t ^ { 2 } + 60 t$$
Find
- the values of \(t\) for which \(P\) is instantaneously at rest
- the distance travelled by \(P\) in the interval \(1 \leqslant t \leqslant 3\)
- the magnitude of the acceleration of \(P\) at the instant when \(t = 3\)