Instantaneous velocity

Definition

Instantaneous velocity is the velocity of an object at a specific moment in time. It is represented as the derivative of the position function with respect to time.

5 Must Know Facts For Your Next Test

1. Instantaneous velocity can be found using the limit definition: $v(t) = \lim_{{\Delta t \to 0}} \frac{{\Delta x}}{{\Delta t}}$.
2. Graphically, instantaneous velocity is the slope of the tangent line to the position-time graph at any given point.
3. Instantaneous velocity is a vector quantity, meaning it has both magnitude and direction.
4. It differs from average velocity, which considers the total displacement over a time interval divided by that time interval.
5. In uniformly accelerated motion, instantaneous velocity can also be calculated using kinematic equations.

Review Questions

• How do you mathematically define instantaneous velocity?
• What is the difference between instantaneous and average velocity?
• How can you determine instantaneous velocity from a position-time graph?

Related terms

Average Velocity:

The total displacement divided by the total time taken.

Acceleration: The rate of change of velocity with respect to time.

Position-Time Graph:

A graph that shows an object's position relative to time; its slope gives the object's instantaneous velocity.