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.

$s(t)=t^4-98t^2+2401,t0$

If appropriate, enter answers in radical form. Use inf to represent $.$

$($a$)$ Find the velocity and acceleration functions.

$v(t)$:$4t^3-196t$

$a(t)$:$12t^2-196$

$($b$)$ Find the position, velocity, speed, and acceleration at $t=5.$

Position $($ft$)$:

Velocity $($ft$/$sec$)$:

Speed $($ft$/$sec$)$: $-480$

Acceleration $(f\frac{t}{se{c}^2})$:

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

$t=$

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

Speeding up:

Slowing down: