Instantaneous Acceleration

Acceleration is in the direction of the change in velocity, but it is not always in the direction of motion. When an object slows down, its acceleration is opposite to the direction of its motion. Although commonly referred to as deceleration, this causes confusion in our analysis as deceleration is not a vector, and does not point to a specific direction with respect to a coordinate system. Therefore, the term deceleration is not used. For example, when a subway train slows down, it accelerates in a direction opposite to its direction of motion. In other words, acceleration is in the negative direction of the chosen coordinate system, so it is said that the train is undergoing negative acceleration. If an object in motion has a velocity in the positive direction with respect to a chosen origin and it acquires a constant negative acceleration, the object eventually comes to a rest and reverses direction.

Instantaneous acceleration, or the acceleration at a specific instant in time, is obtained by the same process as instantaneous velocity—that is, by considering an infinitesimal interval of time. For example, to find instantaneous acceleration using only algebra, we must choose an average acceleration that is representative of the motion.

This text is adapted from Openstax, University Physics Volume 1, Section 3.3: Average and Instantaneous Acceleration.