Instantaneous vs Average Velocity

Velocity tells us how fast an object is moving and in which direction. There are two common ways to describe velocity:

Average Velocity

The average velocity over a time interval is the total displacement divided by the total time taken:

where:

• \( \Delta \vec{x} = \) displacement vector (final position − initial position)
• \( \Delta t = \) elapsed time interval

Average velocity gives a general idea of how fast and in what direction the object moved during the whole time period.

Instantaneous Velocity

The instantaneous velocity is the velocity at a specific moment in time. It is the limit of the average velocity as the time interval approaches zero:

In simpler terms, instantaneous velocity is the derivative of position with respect to time — how fast the position is changing at that exact instant.

Example

Suppose a car travels from 0 m to 100 m in 20 seconds.

• The average velocity is: \( \frac{100\, m - 0\, m}{20\, s} = 5\, m/s \)
• But at any instant, the car’s velocity could be different (for example, accelerating from 0 to 10 m/s).

Visualizing Instantaneous vs Average Velocity