In a softball game, the pitcher throws the $180$g softball at a speed of $34$m$/$s$.$ If it took her $40$ms to accelerate the ball from rest to this speed, find the following$$without using kinematics:

$($a$)$How much work does the pitcher do on the ball?

$($b$)$What is the pitcher's power output during the pitch?

$($c$)$On the next pitch, the ball reaches the same speed but it takes more than $40$ms$.$ Is the power produced by the pitcher in this case more than, less than, or the same as the power found in part $($b$)?$ Explain.