Energy

Energy represents the capacity to do work. Energy is preferable in most circumstances because it is a scalar quantity rather than a vector quantity (see 1D kinematics). Energy is measured in Joules, equivalent to N*m. Types of energy include kinetic, elastic, internal and potential (including gravitational potential) energy. Energy is a large component of thermodynamics. The work done on an object is equal to the area under the curve on a distance vs. force graph. The Law of conservation of energy states that in an isolated system, energy remains constant over time.

Kinetic Energy
Kinetic energy refers to to the energy stored by a moving object. Translational Kinetic energy is defined as:
Uk = 1/2mv^2
where
m = mass
v = velocity

Potential Energy
Gravitational potential energy refers to the energy stored by an object in a gravitational feild and is defined as:
Ug = mgy
where
m = mass
g = gravitational acceleration
y = a vertical distance

Elastic Energy
Elastic energy is the energy stored in an object when it is compressed or stretched. This is defined as:
Ue = 1/2kΔx
where
k = spring constant
Δx = compression distance
Hooke's Law defines the force of a spring as:
F = kΔx
where
k = spring constant
Δx = compression distance







Additional sources:
http://www.scienceaccelerator.gov/