A particle \(P\) moves on the positive \(x\)-axis. The velocity of \(P\) at time \(t\) seconds is \(\left( 2 t ^ { 2 } - 9 t + 4 \right) \mathrm { m } \mathrm { s } ^ { - 1 }\). When \(t = 0 , P\) is 15 m from the origin \(O\).
Find
the values of \(t\) when \(P\) is instantaneously at rest,
the acceleration of \(P\) when \(t = 5\)
the total distance travelled by \(P\) in the interval \(0 \leqslant t \leqslant 5\)