Kinetic energy is energy of motion, equivalent to one-half an object's mass multiplied by its velocity squared. If a body of mass m has an initial velocity u and is accelerated by a constant force F to velocity of v then from Newton's laws of motion, v 2 = u 2 + 2as and the definition of force F = ma, then the work done is equal to Fs.
W = Fs
but F = ma and s = ½a(v 2 - u 2)
so W = ½m(v 2 - u 2)
= ½mv 2 - ½mu 2
If the body starts from rest, u = 0 and so the work done on it would be ½mv 2. This gives the amount of energy that any moving body of mass m traveling at velocity v has.
Compare with potential energy.