The velocity of a body moving in a straight line is increased by applying a constant force F, for some distance in the direction of the motion. Prove that the increase in the kinetic energy of the body is equal to the work done by the force on the body.

Explanation

Consider an object of mass m moving with uniform velocity u.
Let, it now be displaced through a distance s, when a constant force F acts on it in the direction of its displacement.
From the third equation of motion,
`v^(2)=u^(2)+2as`
`rArrv^(2)-u^(2)=2as`
`rArrs=(v^(2)-u^(2))/(2a)" ".....(i)`
We know that, work done by F is
`W=Fscostheta` (since, force and displacement are in same direction so `(theta=0^(@))`
`=ma.s" "[:'F=ma]`
`=ma"xx((v^(2)-u^(2))/(2a))" "[from Eq.(i)]`
`W=(1)/(2)m(v^(2)-u^(2))" "....(ii)`
If the object is starting from its stationary position i.e., `u=0,` from Eq. (ii), we get
`W=(1)/(2)mv^(2)`
If is clear that the work done is equal to the change in the kinetic energy of an object.