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Kinetic Energy and Potential Energy
Kinetic Energy
A body in motion possesses energy. This is called kinetic energy.

This statement is supported by the fact that the body can do work at the expense of its motion.
Wind passing through a wind turbine slows down and as a result we can obtain electrical energy from the generator driven by the turbine.

Remember that "motion" is a relative concept; see the relativity section for more discussion of this idea. In what follows here we will assume that any speeds are measured relative to some local reference body, usually the earth.
In order to find the quantity of energy possessed by a moving body, we find how much work we have to do to get the body moving at the speed it has.

Consider a car being accelerated from rest to speed v in a distance s, as shown below .

For a body starting from rest we have:

Kinetic energy (KE) gained by the body = work done causing it to accelerate.
work done = force × displacement
If the force used to acceleration the car was (on average) of magnitude F then (if we ignore friction and air resistance) we can say that F = ma. So, we have

Therefore

Potential Energy
If a force acts on a body then the body is said to possess potential energy.
For example:
A mass in a gravitational field possesses gravitational potential energy.
A stretched spring possesses elastic potential energy.
A charged body in an electric field possesses electrical potential energy.
The potential energy possessed by a body is equal to the work done putting it into its "energetic state".

Gravitational Potential Energy
Consider a body of mass m being lifted a short distance, h, near the earth's surface, at constant speed.
 At position B the body possesses more GPE because work has been done (against the force of gravity) lifting it from A to B At position A the body possesses GPE (because the force of gravity acts on it)

The increase in the G.P.E. is equal to the work done moving the body from A to B.
If, as stated, the body is lifted at constant speed through the height h then, the force needed to do the work against gravity must be exactly equal in magnitude (and opposite in sense) to mg.
Work done = force × displacement
Therefore the change in GPE (written ∆ GPE) is simply given by

This equation is, of course, only useful if the distance h is small enough to consider that the magnitude of the gravitational field strength, g does not significantly change.
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