Instantaneous velocity

Definition

Instantaneous velocity is the rate of change of an object's position with respect to time at a specific instant. It is the derivative of the position function with respect to time.

5 Must Know Facts For Your Next Test

1. Instantaneous velocity can be found by taking the limit of the average velocity as the time interval approaches zero.
2. Mathematically, instantaneous velocity is represented as $v(t) = \frac{d}{dt} s(t)$, where \(s(t)\) is the position function.
3. The concept of instantaneous velocity requires understanding limits and derivatives from calculus.
4. Unlike average velocity, instantaneous velocity provides information about motion at an exact point in time.
5. The units for instantaneous velocity are typically meters per second (m/s) if using SI units.

Review Questions

• How do you mathematically define instantaneous velocity?
• What calculus concepts are essential for understanding instantaneous velocity?
• Explain how you would find the instantaneous velocity given a position function.

Related terms

Derivative: A measure of how a function changes as its input changes; it represents an instantaneous rate of change.

Limit:

The value that a function approaches as the input approaches some value; fundamental in defining derivatives.

Position Function: $s(t)$ describes an object's location at any given time $t$.