3.3:
Instantaneous Velocity – I
The average velocity of an object cannot tell us how fast or in what direction the object was moving at any given time. To identify this, we need the velocity at a specific instant of time or the instantaneous velocity.
The instantaneous velocity is the limit of the average velocity as the time interval approaches zero, or the derivative of x with respect to t. Here, the variable x is used to describe an object’s position along a one-dimensional motion. Instantaneous velocity is a vector quantity, and the symbol vx is used for instantaneous velocity along the x-direction.
The sign of the instantaneous velocity is the same as the sign of Δx, as time is always considered to be positive. For example, if x increases and the motion is in the positive x-direction, it implies a positive value of instantaneous velocity. Similarly, if x decreases and the motion is in the negative x-direction, instantaneous velocity has a negative value.
3.3:
Instantaneous Velocity – I
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 vx 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.