An armadillo runs along a straight line $($which we call the x$-$axis$).$ The armadillos position as a function of time is x$($t$)=100\mathrm{.}0+10\mathrm{.}00$t $0\mathrm{.}5$t$\mathrm{²}$ m$.$

 

 

 

 $($a$)$ Find the armadillos initial position, initial velocity, and acceleration.

$($b$)$ At what instant of time is the armadillos velocity zero? 

 

 $($c$)$ Does it speed up or slow down at $5$ sec after starting? At $15$ sec$?$ 

 

 $($d$)$ At what time after starting does the armadillo return back to the starting point?  

 

 $($e$)$ Sketch graphs x vs$.$ t$,$ v vs$.$ t$,$ and a vs$.$ t$.$ 

 

 $($f$)$ At what time$($s$)$ is the armadillo at a distance $20\mathrm{.}0$ m from the starting point? $\mathrm{}$$$

 $($g$)$ What is its velocity at each of the times in part $($f$)?$