# Why is my book using different equations to solve for velocity?

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I am having a difficult time trying to figure out why my book says that I should solve for v by:
(1) Set the kinetic energy equal to the change in potential energy and solve for v

Then 3 problems later it says solve for v by:
(2)Set ΔK = −ΔU and solve for v

http://img593.imageshack.us/img593/1995/1idz.jpg [Broken]

I just need to know why they are using different equations to solve for v.. this is not making any sense.

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Homework Helper
I am having a difficult time trying to figure out why my book says that I should solve for v by:
(1) Set the kinetic energy equal to the change in potential energy and solve for v

Then 3 problems later it says solve for v by:
(2)Set ΔK = −ΔU and solve for v

I just need to know why they are using different equations to solve for v.. this is not making any sense.

They are essentially the same equations. ΔK = −ΔU means that the gain in kinetic energy is equal in magnitude to the decrease in potential energy.

The V (upper case) in problem 21 is the potential difference. The v (lower case) is the velocity of the charged particle.

AM

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They are essentially the same equations. ΔK = −ΔU means that the gain in kinetic energy is equal in magnitude to the decrease in potential energy.

But how do I know when to use
ΔK = −ΔU
or
ΔK = ΔU

That is my problem. :'(

Staff Emeritus