An object moves with constant acceleration $3\mathrm{.}80$ m$/$s$2$ and over a time interval reaches a final velocity of $13\mathrm{.}0$ m$/$s$.$

$($a$)$ If its original velocity is $6\mathrm{.}50$ m$/$s$,$ what is its displacement during the time interval?

m

$($b$)$ What is the distance it travels during this interval?

m

$($c$)$ If its initial velocity is

$6\mathrm{.}50$ m$/$s$,$

what is its displacement during this interval?

m

$($d$)$ What is the path length it travels during the interval in part $($c$)?$