In everyday conversation, accelerating means speeding up. Acceleration is a vector in the same direction as the change in velocity, Δv, therefore the greater the acceleration, the greater the change in velocity over a given time. Since velocity is a vector, it can change in magnitude, direction, or both. Thus acceleration is a change in speed or direction, or both. For example, if a runner traveling at 10 km/h due east slows to a stop, reverses direction, and continues their run at 10 km/h due west, their velocity has changed as a result of the change in direction, even though the magnitude of the velocity is the same in both directions. Thus, acceleration occurs when velocity changes in magnitude (an increase or decrease in speed), direction, or both.
The acceleration vector is the instantaneous acceleration, and it can be obtained from the derivative of the velocity function with respect to time. Acceleration varies greatly with different objects and has nothing to do with the size of an object or its mass. Acceleration can also vary significantly with time during the motion of an object. For example, a drag racer has a large acceleration just after its start, but then it tapers off as the vehicle reaches a constant velocity. Its average acceleration can be quite different from its instantaneous acceleration at a particular time during its motion.
This text is adapted from Openstax, University Physics Volume 1, Section 4.2: Acceleration Vector.
