2 A particle moves in a straight line. At time \(t\) seconds, it has velocity \(v \mathrm {~m} \mathrm {~s} ^ { - 1 }\), where
$$v = 6 t ^ { 2 } - 2 \mathrm { e } ^ { - 4 t } + 8$$
and \(t \geqslant 0\).
- Find an expression for the acceleration of the particle at time \(t\).
- Find the acceleration of the particle when \(t = 0.5\).
- The particle has mass 4 kg .
Find the magnitude of the force acting on the particle when \(t = 0.5\).
- When \(t = 0\), the particle is at the origin.
Find an expression for the displacement of the particle from the origin at time \(t\).