A $1500-$kg car accelerates from $10$ m$/$s to $30$ m$/$s over a distance of $200$ meters. A constant frictional force of $400$ N opposes the motion of the car throughout its journey.

$($a$)[10$ pts$]$ Determine the total work done by the engine.

$($b$)[8$ pts$]$ Determine the time taken for the car to travel $200$ meters.$$

$($c$)[4$ pts$]$ Find the average power output of the engine.$$