10 A particle \(P\) is moving in a straight line. At time \(t\) seconds, where \(t \geqslant 0 , P\) has velocity \(v \mathrm {~ms} ^ { - 1 }\) and acceleration \(a \mathrm {~ms} ^ { - 2 }\) where \(a = 4 t - 9\). It is given that \(v = 2\) when \(t = 1\).
- Find an expression for \(v\) in terms of \(t\).
The particle \(P\) is instantaneously at rest when \(t = t _ { 1 }\) and \(t = t _ { 2 }\), where \(t _ { 1 } < t _ { 2 }\).
- Find the values of \(t _ { 1 }\) and \(t _ { 2 }\).
- Determine the total distance travelled by \(P\) between times \(t = 0\) and \(t = t _ { 2 }\).