3.17: Particle with $s=\sqrt{t+\tfrac{1}{3}}-\tfrac{1}{2}$

A particle moves in a straight line such that its displacement, $s$ metres, from a fixed point at time $t$ seconds ($t\geqslant 0$) is
$$s=\left(t+\tfrac{1}{3}\right)^{1/2}-\tfrac{1}{2}.$$

Find the exact speed of the particle when $t=1$.

Show that the acceleration of the particle will never be zero.