How Much Work To Get Speed

Question

A player hit a serve in a racket sport that was clocked at 64 mph. How much work did she have to do on the

8​-oz ball to get it to that​ speed?

Answer 1

I don't know why this is calculus, except that you can derive that work = change in kinetic energy = 1/2 mv²

W = integral of (Fdx = ma dx = m(dv/dt)(dx) = mdv (dx/dt) = mvdv) = 1/2 mv² + C

In this case, it is just a matter of plugging in W = 1/2 mv² (v initial = 0) in metric units where

8oz*(1lb/16 oz)(1kg/2.2 lbs) and

64 miles/hour * (1610 m/mil) (1 hour/3600s)

Plug into formula and W will be in Joules.