The function $s(t)$ describes the position of a particle moving along a coordinate line, where $s$ is in feet and $t$ is in seconds. $$s(t) = t^{4}-162t^{2}+6561, \qquad t \ge 0$$ If appropriate, enter answers in radical form. Use inf to represent $\small{\infty}$.

(a) Find the velocity and acceleration functions.

$\qquad\qquad\quad\;\,v(t)$=
$\qquad\qquad\quad\;\,a(t)$=

(b) Find the position, velocity, speed, and acceleration at $t = 8$.

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

Hint: