A particle, \(P\), moves along the \(x\)-axis. At time \(t\) seconds, \(t \geqslant 0\), the displacement, \(x\) metres, of \(P\) from the origin \(O\), is given by \(x = \frac { 1 } { 2 } t ^ { 2 } \left( t ^ { 2 } - 2 t + 1 \right)\)
Find the times when \(P\) is instantaneously at rest.
Find the total distance travelled by \(P\) in the time interval \(0 \leqslant t \leqslant 2\)
Show that \(P\) will never move along the negative \(x\)-axis.