A force exerts an impulse `J` on a body changing its speed from `u` to `upsilon`. The force and object's motion are along the same line. Show that the work done by the force is `J(u+upsilon)//2`

Explanation

As impulse `=` change in mometum
`J=m(upsilon-u)`
According to work energy theorem,
`W=` increase in K.E. `=(1)/(2)m(upsilon^(2)-u^(2))`
`W=(1)/(2)m(upsilon-u)(upsilon+u)`
Using (i), `W=J(upsilon+u)//2`