$3.$ A robotic arm moves an object with constant acceleration$/$deceleration through three stages in an assembly line, and the velocity of the object as function of time is displayed in the figure to the right. At $\backslash ($ t$=0\backslash$mathrm$\{$~s$\}\backslash )$ the object is located at $\backslash ($ x$=0\backslash$mathrm$\{$~m$\}\backslash ).$ The integral of the velocity gives the change in position.

a$)$ What is the change in position during the first second?

b$)$ What is the change in position between $2$ s and $6$ s $?$

c$)$ At which $\backslash ($ x $\backslash )-$coordinate is the object at $12$ s $?$

d$)$ Find $\backslash (\backslash$int$\_\{6\}^\{9\}-2$ v$($t$)$ d t $\backslash ).$

b$)$ Assuming the movement happens in one dimension only, does the object ever return to its starting point? $(15$ p$)$