1. What is the Resultant Velocity Equation?

The resultant velocity equation \( v = \sqrt{u^2 + 2 a s} \) calculates the final velocity of an object undergoing constant acceleration, given its initial velocity, acceleration, and distance traveled. This kinematic equation is fundamental in physics for motion analysis.

2. How Does the Calculator Work?

The calculator uses the resultant velocity equation:

Where:

• \( v \) — Final velocity (m/s)
• \( u \) — Initial velocity (m/s)
• \( a \) — Constant acceleration (m/s²)
• \( s \) — Distance traveled (m)

Explanation: The equation combines the initial velocity with the velocity gained through acceleration over distance, accounting for both the direction and magnitude of motion.

3. Importance of Resultant Velocity Calculation

Details: Calculating resultant velocity is essential for solving motion problems in physics, engineering applications, vehicle safety analysis, and projectile motion studies.

4. Using the Calculator

Tips: Enter initial velocity (can be positive, negative, or zero), acceleration (positive for speeding up, negative for slowing down), and distance (must be ≥0). All values must be valid numbers.

5. Frequently Asked Questions (FAQ)

Q1: What if acceleration is zero?
A: With zero acceleration, the equation simplifies to v = u (velocity remains constant).

Q2: Can this be used for deceleration?
A: Yes, use negative acceleration values for deceleration scenarios.

Q3: What are the units for each variable?
A: All values should be in consistent SI units (m/s for velocity, m/s² for acceleration, m for distance).

Q4: When is this equation not applicable?
A: This assumes constant acceleration in a straight line. For variable acceleration or curved paths, more complex equations are needed.

Q5: How does initial velocity direction affect the result?
A: The equation accounts for direction through the sign of u and a. Positive/negative results indicate direction of motion.