Question

derive the formula for the kinetic enenrgy of an object of mass m moving velocity v?

Answer 1

The body is brought to rest by a force F and retardation produced be a and the body travels distance S before coming to a stop . the rest is in the picture

Answer 2

The kinetic energy of a moving body is measured by the amount of work which has been done in bringing the body from the rest position to its present position
Let a body of mass m be in rest position. When we apply a constant force F on the body it starts moving under acceleration . If a be the acceleration then by newton's second law we have
a=F/m
Suppose a body acquires a velocity in moving a distance s. According to the reaction v^2=2as=2×(F/m)×s
....... F×s=1/2 mv^2
But force × displacement is the work which thevforce has done on body... So
K=W=1/2 mv^2