# Kinetic Energy

Kinetic energy (abbreviated to KE below - but don't you dare do that in an exam paper!) is the energy of motion or movement energy.

There are three forms of KE

vibrational (the energy due to vibrational motion),

rotational (the energy due to rotational motion), and

translational (the energy due to motion from one location to another).

Generally at KS3 and 4 we consider translational kinetic energy when we look at kinetic energy

The Translational Kinetic Energy (you can just call it kinetic energy!) of an object depends on how fast the object is moving, the faster it goes the higher the kinetic energy it has. If it is stationary it has no kinetic energy!

KE also depends on the mass of the object.

# EK = ½mv2

Where

Ek = kinetic energy (in joule)

m = mass (in kg)

v = velocity in m/s

### Derivation of the equation

The change in kinetic energy is the work done due to movement

∆EK = W

But work done is the force x distance moved

W = F∆s

and we know that F = ma

So

∆EK = ma∆s

Now consider an object falling from rest under constant acceleration to a speed v

Newton's Equation of motion gives us:

v2 = u2 + 2a∆s

But

u = 0 m/s

So

2a∆s = v2

a∆s = ½v2

and therefore substituting into EK = ma∆s, we get:

# EK = ½mv2

This equation shows us that the kinetic energy of an object is directly proportional to its mass and to the square of its speed.

That means if you double the mass - you double the KE, triple the mass - triple the KE etc. The KE depends on the mass.

It also means that for a doubling speed, the KE will increase by a factor of four; for a triple increase in speed, the KE will increase by a factor of nine; etc. The KE is dependent upon the square of the speed.

KE (like all forms of energy!) is a scalar quantity - it has magnitude (size) but no direction.