1. What is Instantaneous Velocity?

Instantaneous velocity is the velocity of an object at a specific moment in time, represented by the slope of the tangent line to the position-time curve at that point. It differs from average velocity by measuring the exact speed and direction at one instant.

2. How Does the Calculator Work?

The calculator uses the slope formula between two points on the tangent line:

Where:

• \( v \) — Instantaneous velocity (m/s)
• \( (x_1, y_1) \) — First point on the tangent line
• \( (x_2, y_2) \) — Second point on the tangent line

Explanation: The closer the two points are to each other, the more accurate the approximation of the instantaneous velocity at that point.

3. Importance of Instantaneous Velocity

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

4. Using the Calculator

Tips: Enter coordinates of two points on the tangent line to your position-time curve. For best results, choose points very close to each other near the point of interest.

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 one specific instant.

Q2: What if my two points are the same?
A: The calculator requires two distinct points to calculate slope. If points are identical, the slope is undefined.

Q3: How accurate is this method?
A: Accuracy improves as the points get closer together. For exact values, calculus (derivatives) would be needed.

Q4: Can this be used for non-linear motion?
A: Yes, as long as you're finding the slope of the tangent line at a specific point on the curve.

Q5: What units should I use?
A: Consistent units are required. Typically meters for position and seconds for time, giving m/s for velocity.