Help with Potential Energy Curve question

Caps1394

1. The problem statement, all variables and given/known data
A conservative force F(x) acts on a 3.0 kg particle that moves along the x axis. The potential energy U(x) associated with F(x) is graphed in Figure 8-60. When the particle is at x = 3.0 m, its velocity is -1.0 m/s. The "kinks" in the graph occur at (1, -2.8), (4, -17.2), and (8.5, -17.2); and the endpoint is at (15, -2).

(a) What are the magnitude and direction of F(x) at this position?
Magnitude
(b) Between what limits of x does the particle move?
Lower limit and and upper limit
(c) What is its speed at x = 7.0 m?

2. Relevant equations
K_e=1/2MV²


3. The attempt at a solution
I'm not even sure how to start this problem
1. The problem statement, all variables and given/known data



2. Relevant equations



3. The attempt at a solution

Delphi51

What does the derivative or slope on the graph represent? That should give you a good start!

Caps1394

That was easy enough!

But about the limits. Would the lower and upper limits be the points where the particle oscillates between?

SammyS

Apparently, you've answered this question to yourself. It will be hard to help you if you don't respond with the answer and why or how you came up with that answer.

Delphi51

"Would the lower and upper limits be the points where the particle oscillates between?"

Yes. This part is a bit complicated but your use of "oscillates" indicates you know what is going on. Kind of like an atom in the potential well of a molecule. Just a matter of calculating the energy it has and using the graph, I think.