We continued our discussion of 1-d motion in a potential. Discussed particle's shifting energy balance between kinetic and potential energy, and noted turning points when E=V. Discussed how the particle's speed varies with position, traveling at locally maximal and minimal speeds when the potential is locally minimal and maximal, respectively. We practiced plotting x(t) and v(x), ending with some general pointers on visualizing functions (using asymptotes, local maxima and minima, and reflection symmetry to construct the function's shape).
We finished by showing that motion in a potential V(x) is exactly the same as motion on a roller coaster with height h(x) = V(x)/(mg). You thus have a lot of physical intuition about the features of motion in a potential; you should always use it as a common sense check on your work!
-- KB