A time$-$dependent force

~F $=$

$($

$8\mathrm{.}00$i $4\mathrm{.}00$t$$j

$)$

N

is exerted on a $2\mathrm{.}00$ kg object initially at rest.

$($a$)$ At what time will the object be moving with a speed of $15\mathrm{.}0$ m$/$s$?$

$($b$)$ How far is the object from its initial position when its speed is $15\mathrm{.}0$ m$/$s$?$

$($c$)$ Through what total displacement has the object traveled at this moment?