A body moving with speed v possesses kinetic energy. The value of the KE is equal to the amount of work needed to bring that body from rest to the speed v and an expression for its value can be found as follows.

Consider a body of mass m which starts from rest and reaches a speed v after moving through a distance s under the action of a constant force F.

 

 

 

 

 

 

 

The acceleration, a, is given by

Then Newton's Law, F= ma, gives

Now Fs is the work done in producing the kinetic energy, therefore 1/2mv^2 is the value of the kinetic energy,

i.e. for a body of mass m moving with speed v,

Note that both m and are always positive quantities showing that KE is always positive and does not depend upon the direction of motion, i.e. kinetic energy is a scalar quantity.