Can potential energy be greater than total energy?

[thomasb1215]

I'm working on a homework problem which states:

"Some object, starting from far down the negative x-axis and moving in the positive x direction, experiences a force, the potential energy U of which is modeled by the function U = 2e^(-x^2), where x is in meters and U is in Joules. The total energy E of the object remains constant at E = 1J. Describe the motion of the object."

The problem isn't worded that well but I take it to mean the potential energy of the object, not of the force.

Relevant equations:
E = U + K
ΔU + ΔK = 0

I understand everything up until the point where U = 1. I know that the greater the potential energy gets, the lesser the kinetic energy gets due to conservation of energy. Thus, the object will slow down as U gets larger and speed up as U gets smaller. When U is greater a than 1, however, K would have to be negative for E to remain constant, which I know is not possible, so I am confused. Am I overlooking something that has to do with the force applied to the object?

Thanks in advance for the help.

 

[haruspex]

When U is greater a than 1..., which I know is not possible,

Exactly. So what does that tell you about the motion of the object?

 

[thomasb1215]

My guess would be that it's not moving, but I'm still not sure how that makes sense in the E = U + K equation.

 

[haruspex]

My guess would be that it's not moving

It tells you more than that.
You wrote, correctly:

... U is greater than 1, however, ... is not possible

Think about this: if you throw a stone up at 1m/s, what will be its speed when it reaches an altitude of 1km?

 

[thomasb1215]

So it never gets there in the first place.

 

[haruspex]

So it never gets there in the first place.

Indeed.