1. What is Instantaneous Velocity?

Instantaneous velocity is the velocity of an object at a specific moment in time. It's determined by calculating the slope of the tangent line to the position-time curve at that point.

2. How Does the Calculator Work?

The calculator approximates instantaneous velocity by calculating the slope between two close points:

Where:

• \( \Delta y \) — Change in position (meters)
• \( \Delta x \) — Change in time (seconds)
• \( v \) — Instantaneous velocity (m/s)

Explanation: The closer the two points are to each other, the better this approximation becomes for the true instantaneous velocity.

3. Importance of Instantaneous Velocity

Details: Instantaneous velocity is crucial in physics for understanding an object's motion at specific moments, analyzing acceleration, and solving problems in kinematics.

4. Using the Calculator

Tips: Enter coordinates of two points very close to each other on the position-time curve. For better accuracy, choose points as close as possible to the moment of interest.

5. Frequently Asked Questions (FAQ)

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

Q2: What if my two points are the same?
A: The calculator requires two distinct points to calculate a slope. Choose points that are very close but not identical.

Q3: How accurate is this approximation?
A: The accuracy improves as the points get closer together. For exact values, calculus (derivatives) is needed.

Q4: Can I use this for non-linear motion?
A: Yes, but remember this gives an approximation. The actual instantaneous velocity would require the derivative of the position function.

Q5: What units should I use?
A: Consistent units are important. Typically position in meters and time in seconds will give velocity in m/s.