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.

The function $\small{s(t)}$ describes the position of a particle moving along a coordinate line, where $s$ is in feet and $t$ is in seconds.

$\small{s(t) = t^{3}-10t^{2}+25t+9, \qquad t \ge 0}$

 

(a) Find the velocity and acceleration functions.

$v(t)$: 3t^2 - 20t + 25

$a(t)$: 6t - 20

 

(b) Over what interval(s) is the particle moving in the positive direction? Use inf to represent $\small{\infty}$, and U for the union of sets.

Interval: 

 

(c) Over what interval(s) is the particle moving in the negative direction? Use inf to represent $\small{\infty}$, and U for the union of sets.

Interval: 

 

(d) Over what interval(s) does the particle have positive acceleration? Use inf to represent $\small{\infty}$, and U for the union of sets.

Interval: 

 

(e) Over what interval(s) does the particle have negative acceleration? Use inf to represent $\small{\infty}$, and U for the union of sets.

Interval: 

 

(f) Over what interval is the particle speeding up? Slowing down? Use inf to represent $\small{\infty}$, and U for the union of sets.

Speeding up: 

Slowing down: