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. $$\small{s(t) = t^{4}-18t^{2}+81, \qquad t \ge 0}$$ If appropriate, enter answers in radical form. Use inf to represent $\small{\infty}$.

(a) Find the velocity and acceleration functions.

$\qquad\qquad\quad\;\,\small{v(t)}$:
$\qquad\qquad\quad\;\,\small{a(t)}$:

(b) Find the position, velocity, speed, and acceleration at $\small{t = 2}$.

Position (ft):
Velocity (ft/sec):
Speed (ft/sec):
Acceleration (ft/sec$\small{^2}$):

(c) At what times is the particle stopped? Enter as a comma-separated list.

$\qquad\qquad\quad\;\;\,\small{t}$

=

(d) When is the particle speeding up? Slowing down? Enter using interval notation.

$\qquad$ Speeding up:
$\qquad$Slowing down: