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.