# Potential and kinetic energy

1. Dec 17, 2008

### lax1113

1. The problem statement, all variables and given/known data
The U of a 4kg object is given by U= 3x^2-x^3 for x smaller than or equal to 3. U is equal to 0 for all numbers larger than 3. If the total energy of the object is 12J what is its speed at 2 meters?

2. Relevant equations
K(x)=E-u(x) E=mechanical energy
K(x)=1/2mv^2

3. The attempt at a solution
It seems like i would plug 2 into the u equation and get the value of U at that particular moment, then use the E, which would be 12??? and subtract the U from it.
I ended up with the answer 2m/s but I could have sworn doing something with integrals for a problem similar to this so it seems like this would be too easy.

thanks

2. Dec 17, 2008

### buffordboy23

No, your approach and answer are correct. In class, you may have used an integral to determine the function for the potential from a given function for the force...make any sense?

Another idea is to graph your potential function U(x). Then draw the line for your energy, E = 12J. The difference between E and U(x) is the kinetic energy at position x. If E < U(x), then the object cannot be located at this position, since the kinetic energy would be of negative value.

3. Dec 18, 2008

### lax1113

Thanks you very much Bufford,
I remember when we used integrals now.