In class Monday we discussed what makes a conservative force and its dependence on position (but not path). This allows us to relate v(x) to position, and hence using our usual trick dx to dt. These questions ask you to think about a probability distribution for a classical particle.
In your own words, what is a probability distribution?
What do you think is the most important quantity to determine the classical probability distribution of a bound system?
Consider a classical particle, with an initial velocity, v, confined to move freely in a well of length L (there are infinite potential energy walls at x = 0 and x = L. What does the particle's relative probability distribution (both in position and velocity) look like?