K.E. = ½ mv²

Units: J, joules

Kinetic energy stored in an object that is moving equals the amount of work done accelerating it from stationary to that speed.

Work done = force x displacement

But F = ma, and displacement = s

So Work done = mas

Remember v² = u² + 2as

Reorganise v² - u² = 2as

But if the object is stationary at the start, u=0, so,

v² = 2 as

This makes = as

But W = m . as

So W = m .

Or Work done = Ek =

E_p = P.E. = mgh

Units: J, Joules

Potential Energy is the energy stored in objects which have been lifted against a gravitational field (or you can also have potential energy in magnetic or electric fields - see later).

The work done lifting them = potential energy stored in them

Work done = Force x displacement

Here the force = weight = m x g

And the diplacement = height = h

So Work done = m x g x h = P.E. gained

Note: this equation only applies if g remains constant. This is true for any movement near the Earth's surface.