The momentum p of an object is the product of its mass m and its velocity v, that is, p=mv. Suppose an object, moving along a straight line, is acted on by a force F=F(t) that is a continuous function of time.

a). Show that the change in momentum over a time interval [tsub0, tsub1] is equal to the integral of F from tsub0 to tsub1; that is, show that p(tsub1) - p(tsub0) = the integral from tsub0 to tsub1 F(t)dt.

b). If a pitcher throws a 90 mi/hr fastball to a batter, who hits a line drive directly back to the pitcher.The ball is in contact with the bat for 0.001 s and leaves the bat with velocity 110 mi/hr. A baseball weighs 5 oz and, in U.S Customary units, its mass is measured in slugs: m=w/g where g= 32 ft/s squared. Show steps to find the change in the balls momentum, and show steps to find the average force on the bat.