# kinetic energy

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} +
2*as* and the definition of force *F* = *ma*, then
the work done is equal to *Fs*.

*W* = *Fs*

but *F* = *ma* and *s* = ½*a*(*v*^{ 2} - *u*^{ 2})

so *W* = ½*m*(*v*^{ 2} - *u*^{ 2})

= ½*mv*^{ 2} - ½*mu *^{2}

If the body starts from rest, *u* = 0 and so the work done on it
would be ½*mv*^{ 2}. This gives the amount of energy
that any moving body of mass *m* traveling at velocity *v* has.

Compare with potential energy.