Solutions to Homework Assignment 1. You're riding on a playground swing. You're traveling back and forth once every few seconds.
Velocity is zero at the two highest points.
For velocity to be zero, you must not have any kinetic energy, which means that all of your energy is potential, which happens at the two highest points of motion. The kinetic energy is maximum when the potential energy is at a minimum, or zero. This happens at the lowest point of the swing's motion, the half-way point between the peaks. It is equal to your weight. If it were less, the ropes would break.