A particle moves along the x-axis, its position given by $x(t) = \dfrac{t}{1+t^2}, \; t \geq 0$, where $t$ is measured in seconds and $x$ in meters.
(a) Find the acceleration at time $t$.
(b) When is the particle speeding up?
(c) When is the particle slowing down?

(a) $a(t) =$
(b) $< t <$
(c) $< t <$ and $t>$