$7.(6$ points$)$ A particle begins by moving to the right along a horizontal line. The graph of the position function $\backslash ($ s$($t$)\backslash )$ is shown. Here $\backslash ($ s$($t$)\backslash )$ is position in meters and $\backslash ($ t $\backslash )$ is time in seconds.

$($a$)$ What is the average velocity of the particle on the interval from $\backslash ($ t$=1\backslash )$ to $\backslash ($ t$=7\backslash )?$ Include units with your answer.

$($b$)$ What is the instantaneous velocity of the particle when $\backslash ($ t$=5\backslash )?$ Include units with your answer.

$($c$)$ When is the particle moving to the right? Moving to the left? Stopped?

$($d$)$ Draw a graph of the velocity function $\backslash ($ v$($t$)\backslash ).$

$($e$)$ Is the velocity function continuous?