\begin{enumerate} \item A heavy ball, of mass 2 kg , rolls along a horizontal surface. It strikes a vertical wall at a speed of \(4 \mathrm {~ms} ^ { - 1 }\) and rebounds. The coefficient of restitution between the ball and the wall is \(0 \cdot 4\). Find the kinetic energy lost in the impact. \item The velocity, \(v \mathrm {~ms} ^ { - 1 }\), of a particle at time \(t \mathrm {~s}\) is given by \(v = 4 t ^ { 2 } - 9\).

1. Find the acceleration of the particle when it is instantaneously at rest.
2. Find the distance travelled by the particle from time \(t = 0\) until it comes to rest. \item A particle \(P\) moves in a plane such that its position vector \(\mathbf { r }\) metres at time \(t\) seconds, relative to a fixed origin \(O\), is \(\mathbf { r } = \mathrm { e } ^ { t } \mathbf { i } - 2 t \mathbf { j }\).