2. A particle of mass 0.5 kg is moving under the action of a single force \(\mathbf { F N }\) so that its velocity \(\mathrm { v } \mathrm { ms } ^ { - 1 }\) at time \(t\) seconds is given by $$\mathbf { v } = 3 t ^ { 2 } \mathbf { i } - 8 t \mathbf { j } + 2 \mathrm { e } ^ { - t } \mathbf { k }$$

1. Find an expression for the acceleration of the particle at time \(t \mathrm {~s}\).
2. Determine an expression for F.v at time \(t \mathrm {~s}\).
3. Find the kinetic energy of the particle at time \(t \mathrm {~s}\).
4. Describe the relationship between the kinetic energy of a particle and the rate of working of the force acting on the particle. Verify this relationship using your answers to part (b) and part (c).