Problem: For the pulley system shown, a force is applied to lift the weight W. What is the relationship between the position, velocity, and acceleration of a point on the cord (point B) to the position, velocity, and acceleration of the weight (same as the pulley - point A)?

Solution:  As point B moves through, say, 20 cm, the amount of the cord's length that gets pulled through comes from both sides of pulley A. Thus, pulley A moves up by half the amount that point B moves. Writing this relationship, and then taking the derivatives...