The function $\small{s(t)}$ describes the position of a particle moving along a coordinate line, where $\small{s}$ is in feet and $\small{t}$ is in seconds. $$\small{s(t) = 6t^{2}-30t, \qquad t \ge 0}$$

(a) Find the velocity and acceleration functions.

$\small{v(t)}$:
$\small{a(t)}$:

(b) Over what interval is the particle moving in the positive direction? Use inf to represent $\small{\infty}$.

Interval:

(c) Over what interval is the particle moving in the negative direction? Use inf to represent $\small{\infty}$.

Interval:

(d) Over what interval is the particle speeding up? Slowing down? Use inf to represent $\small{\infty}$.

Speeding up:
Slowing down: