Final answer:
The pendulum swings the fastest at the lowest point of its arc because all the potential energy is converted to kinetic energy due to gravity.
Step-by-step explanation:
When discussing the motion of a simple pendulum, which is a particle of mass m suspended by a massless string of a certain length, and released from rest at a given angle, the point at which the pendulum swings the fastest is at the lowest point of its arc. This is due to the conversion of potential energy at the highest point into kinetic energy at the lowest point.
When the pendulum is released, gravity causes it to accelerate towards the equilibrium position, where the string is vertical. Since air resistance and friction at the pivot are ignored, the potential energy lost as the pendulum falls is entirely converted into kinetic energy. Therefore, at the very bottom of the swing, all the potential energy that has been lost is now in the form of kinetic energy, resulting in the maximum speed of the pendulum.