Ok, I've been trying to soak up the MIT physics material, but I am stuck on something and it is driving me crazy. They have several questions about graphs of potential energy vs. position, which also includes the total mechanical energy. I just can't fully wrap my mind around these graphs and the explanations they give about them are extremely convoluted. Questions 5-9 on here are what I'm talking about: http://ocw.mit.edu/courses/physics/8-01sc-physics-i-classical-mechanics-fall-2010/conservation-of-energy/mechanical-energy-and-the-simple-harmonic-oscillator/MIT8_01SC_quiz15.pdf What is confusing me is how you determine which direction the object will head based on the graph alone? I understand that when potential decreases, kinetic will increase. However, for question 5 on that PDF, they indicate that the object would go to infinity. What I don't get is how you don't know that it doesn't just stop when it gets to the position that is directly on the mechanical energy line? What lets you know that the motion would stop there and change direction, or does it not even get there for some reason? Also, what happens to the kinetic energy when the position goes to the point where potential is above the overall mechanical? Since kinetic is scalar, wouldn't it be impossible for it to become negative? If that's the case, then wouldn't a potential higher than the mechanical be impossible? If someone could please make these types of graphs make sense to me, I'd really appreciate it.