# Relation between work, kinetic energy and potential energy

We derived two equations in class.

1. The work done between two points $A$, $B$ is equal to the difference between the kinetic energy at the last point and the one at the first point.
2. The work done between two points $A$, $B$ is equal to the difference between the potential energy at the first point and the one at the last point.

Now the thing is the following: if I have a car driving with constant velocity on the street and I use some work to accelerate it, then it is driving with a higher speed, so the kinetic energy will have been changed the way we said. But the potential energy is left unchanged, so I was wondering: when are these two equations true and when are they not applicable?

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Actually, the potential energy of the car has decreased, but in a less obvious way than you're probably used to. I assume you have only encountered work in the context of newtonian mechanics so far and haven't learned much about thermodynamics? The potential energy that has been decreased in the car is the bond energy of the fuel. Fuel is being 'burned', i.e. bonds are being broken, and the energy that is released by this process is used to perform work. There's also losses from friction etc, but the total energy is conserved. –  Wouter Jun 27 '13 at 8:46
actually, I wanted to know when both equations are applicable. So, thank you that you are all posting something that has to do with my example but that was just to make clear, that I am not sure that both equations are always valid. –  Xin Wang Jun 27 '13 at 8:55
I've turned my comment into an answer with more emphasis on the actual validity of the statements in your question. Let me know if you're still unsure. –  Wouter Jun 27 '13 at 9:22
thank you. it is perfect now –  Xin Wang Jun 27 '13 at 9:23
You're welcome ;-) –  Wouter Jun 27 '13 at 9:24