The average velocity during a time interval cannot tell us how fast or in what direction a particle is moving at any given time during the interval. To calculate this, it is important to know the instantaneous velocity, which is the velocity at a specific instant of time or at a specific point along the path. Instantaneous velocity is the quantity that measures how fast an object is moving along its path. In other words, the instantaneous velocity v_x of an object is the limit of the average velocity as the elapsed time approaches zero, or the derivative of x with respect to t.

Like average velocity, the instantaneous velocity is a vector with the dimensions of length per unit of time. Instantaneous velocity can have both positive and negative values. A positive value of instantaneous velocity implies increasing x, and the motion is in the positive x-direction. A negative value of instantaneous velocity implies decreasing x, and the motion is in the negative x-direction.

Instantaneous speed is the magnitude of the instantaneous velocity. For example, a particle with instantaneous velocity −10 m/s and a particle with instantaneous velocity +10 m/s have the same instantaneous speed, but are traveling in opposite directions.

This text is adapted from Openstax, University Physics Volume 1, Section 3.2: Instantaneous Velocity and Speed.