1 A particle moves in a straight line and at time \(t\) seconds has velocity \(v \mathrm {~m} \mathrm {~s} ^ { - 1 }\), where
$$v = 6 t ^ { 2 } + 4 t - 7 , \quad t \geqslant 0$$
- Find an expression for the acceleration of the particle at time \(t\).
- The mass of the particle is 3 kg .
Find the resultant force on the particle when \(t = 4\).
- When \(t = 0\), the displacement of the particle from the origin is 5 metres.
Find an expression for the displacement of the particle from the origin at time \(t\).