Total Potential and kinetic energy

[lax1113]

Homework Statement

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?

Homework Equations

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

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.

Any advice?

thanks

 

[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.

 

[lax1113]

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