What is Energy?
Common Units of Energy
SI:
Newton meter (Nm)
1 Nm = 1 J
Joule (J)
1 J = 0.239 cal
Calorie (cal)
1 cal = 4.184 J
Watt hours (Wh)
1 Wh = 3,600 J
Kilowatt hours (kWh)
1 kWh = 1,000 Wh
1 kWh = 3,600,000 J
1 kWh = 3,412 BTU
English:
Foot  pound (ft lb)
1 ft lb = 1.356 Nm
British Thermal Unit (BTU)
1 BTU = 1,055 J
1 BTU = 0.0002931 kWh

Energy is the final chapter in our terminology saga. We'll need everything we've learned up to this point to explain energy.
If power is like the strength of a weightlifter, energy is like his endurance. Energy is a measure of how long we can sustain the output of power, or how much work we can do. Power is the rate at which we do the work. One common unit of energy is the kilowatthour (kWh). You learned in the last section that a kW is a unit of power. If we are using one kW of power, a kWh of energy will last one hour. If we use 10 kW of power, we will use up the kWh in just six minutes.
There are two kinds of energy: potential and kinetic.
Potential Energy
Potential energy is waiting to be converted into power. Gasoline in a fuel tank, food in your stomach, a compressed spring, and a weight hanging from a tree are all examples of potential energy.
The human body is a type of energyconversion device. It converts food into power, which can be used to do work. A car engine converts gasoline into power, which can also be used to do work. A pendulum clock is a device that uses the energy stored in hanging weights to do work.
When you lift an object higher, it gains potential energy. The higher you lift it, and the heavier it is, the more energy it gains. For example, if you lift a bowling ball 1 inch, and drop it on the roof of your car, it won't do much damage (please, don't try this). But if you lift the ball 100 feet and drop it on your car, it will put a huge dent in the roof. The same ball dropped from a greater height has much more energy. So, by increasing the height of an object, you increase its potential energy.
Let's go back to our experiment in which we ran up the stairs and found out how much power we used. There is another way to look at how we calculated our power: We calculated how much potential energy our body gained when we raised it up to a certain height. This amount of energy was the work we did by running up the stairs (force * distance, or our weight * the height of the stairs). We then calculated how long it took to do this work, and that's how we found out the power. Remember that power is the rate at which we do work.
The formula to calculate the potential energy (PE) you gain when you increase your height is:
PE = Force * Distance
In this case, the force is equal to your weight, which is your mass (m) * the acceleration of gravity (g), and the distance is equal to your height (h) change. So the formula can be written:
PE = mgh
Kinetic Energy
Kinetic energy is energy of motion. Objects that are moving, such as a roller coaster, have kinetic energy (KE). If a car crashes into a wall at 5 mph, it shouldn't do much damage to the car. But if it hits the wall at 40 mph, the car will most likely be totaled.
Kinetic energy is similar to potential energy. The more the object weighs, and the faster it is moving, the more kinetic energy it has. The formula for KE is:
KE = 1/2*m*v^{2},
where m is the mass and v is the velocity.
One of the interesting things about kinetic energy is that it increases with the velocity squared. This means that if a car is going twice as fast, it has four times the energy. You may have noticed that your car accelerates much faster from 0 mph to 20 mph than it does from 40 mph to 60 mph. Let's compare how much kinetic energy is required at each of these speeds. At first glance, you might say that in each case, the car is increasing its speed by 20 mph, and so the energy required for each increase must be the same. But this is not so.
We can calculate the kinetic energy required to go from 0 mph to 20 mph by calculating the KE at 20 mph and then subtracting the KE at 0 mph from that number. In this case, it would be 1/2*m*20^{2}  1/2*m*0^{2}. Because the second part of the equation is 0, the KE = 1/2*m*20^{2}, or 200 m. For the car going from 40 mph to 60 mph, the KE = 1/2*m*60^{2}  1/2*m*40^{2}; so KE = 1,800 m  800 m, or 1000 m. Comparing the two results, we can see that it takes a KE of 1,000 m to go from 40 mph to 60 mph, whereas it only takes 200 m to go from 0 mph to 20 mph.
There are a lot of other factors involved in determining a car's acceleration, such as aerodynamic drag, which also increases with the velocity squared. Gear ratios determine how much of the engine's power is available at a particular speed, and traction is sometimes a limiting factor. So it's a lot more complicated than just doing a kinetic energy calculation, but that calculation does help to explain the difference in acceleration times.