Final answer:
At the lowest point in the swing of a simple pendulum, gravity provides centripetal acceleration, changing the direction of motion but not the speed. Therefore, although the pendulum does not stop accelerating entirely at any point, the component of acceleration that affects speed (tangential acceleration) is zero at the lowest point.
Step-by-step explanation:
Acceleration of a Pendulum
When discussing a simple pendulum, it is important to understand that the acceleration is not constant throughout the pendulum's swing. At the highest point, the pendulum has the highest potential energy and zero kinetic energy if it is released from rest. As it swings downwards, it gains speed and kinetic energy until it reaches the lowest point of its arc where it has the maximum kinetic energy and minimum (theoretically zero) potential energy. Here, the pendulum's speed is the greatest, and it momentarily has only horizontal velocity, implying that the acceleration due to gravity is perpendicular to the velocity, causing the pendulum to change direction rather than speed.
At the lowest point in the swing, the entire force of gravity is used to change the direction of the pendulum's velocity, and it does not speed up or slow down the pendulum for a brief moment. Therefore, the acceleration of the pendulum is not zero anywhere in the path, because even at the lowest point, gravity is providing centripetal acceleration to change the pendulum's direction. However, if we consider the component of acceleration that contributes to the pendulum's speed (tangential acceleration), then at the lowest point, the tangential acceleration is indeed zero because all of gravity's force is directed towards changing direction (centripetal), and none is being used to speed it up or slow it down (tangential).