3. At time \(t\) seconds the acceleration, \(a \mathrm {~ms} ^ { - 2 }\), of a particle is given by
$$a = \frac { 4 } { ( 1 + t ) ^ { 3 } }$$
When \(t = 0\), the particle has velocity \(1 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) and displacement 3 m from a fixed origin \(O\).
- Find an expression for the velocity of the particle in terms of \(t\).
- Show that when \(t = 3\) the particle is 10.5 m from \(O\).