At time \(t\) s, a particle travelling in a straight line has acceleration

\((2t+1)^{-\frac12}\text{ m s}^{-2}.\)

When \(t=0\), the particle is \(4\) m from a fixed point \(O\) and is travelling with velocity \(8\text{ m s}^{-1}\) away from \(O\).

(a) Find the velocity of the particle at time \(t\) s.

(b) Find the displacement of the particle from \(O\) at time \(t\) s.