Kinetic Energy

When a body of mass m moves with speed v, it has kinetic energy. This is given by E = mv2/2. We shall now derive this formula from the definition of work done.

Suppose I push the body along a perfectly smooth table, with force F. The body accelerates over a distance d. The work done is Fd. This work produces only kinetic energy. No heat is produced since there is no friction.

From Newton's second law, F = ma. So E = Fd = mad.

Recall the acceleration equation v2 - u2 = 2as. s is our distance d.

If the body is initially at rest, u = 0. Then v2 = 2ad, or ad = v2/2.

So the kinetic energy becomes E = mad = mv2/2. This is the formula.


Copyright 2010 by Kai Hock. All rights reserved.
Last updated: 19 September 2010.