1. What is Instantaneous Velocity?

Instantaneous velocity is the velocity of an object at a specific moment in time. It's the limit of the average velocity as the time interval approaches zero, represented mathematically as the derivative of position with respect to time.

2. How Does the Calculator Work?

The calculator uses the instantaneous velocity formula:

Where:

• \( v \) — Instantaneous velocity (m/s)
• \( ds \) — Change in displacement (m)
• \( dt \) — Change in time (s)

Explanation: This formula calculates the rate of change of position with respect to time at a specific instant.

3. Importance of Instantaneous Velocity

Details: Instantaneous velocity is crucial in physics for understanding motion at precise moments, analyzing acceleration, and solving problems in kinematics and dynamics.

4. Using the Calculator

Tips: Enter the change in displacement in meters and the change in time in seconds. The time interval must be greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: How is instantaneous velocity different from average velocity?
A: Average velocity is total displacement over total time, while instantaneous velocity is the velocity at a specific moment.

Q2: What if dt approaches zero?
A: In calculus, this becomes the derivative of position with respect to time, giving the exact instantaneous velocity.

Q3: Can this be used for non-constant acceleration?
A: This calculator gives average velocity over small intervals. For non-constant acceleration, you'd need the position function's derivative.

Q4: What are typical units for instantaneous velocity?
A: The SI unit is meters per second (m/s), but any distance/time unit combination can be used.

Q5: How does this relate to tangent lines on position-time graphs?
A: The slope of the tangent line to the position-time curve at a point equals the instantaneous velocity at that time.