3 A particle moves in a straight line and at time \(t\) has velocity \(v\), where
$$v = 2 t - 12 \mathrm { e } ^ { - t } , \quad t \geqslant 0$$
- Find an expression for the acceleration of the particle at time \(t\).
- State the range of values of the acceleration of the particle.
- When \(t = 0\), the particle is at the origin.
Find an expression for the displacement of the particle from the origin at time \(t\).
(4 marks)