1. What is the Final Velocity Equation?

The final velocity equation \( v = \sqrt{u^2 + 2 a s} \) calculates the final velocity of an object without knowing the time, using initial velocity, acceleration, and displacement. This is derived from the equations of motion.

2. How Does the Calculator Work?

The calculator uses the final velocity equation:

Where:

• \( v \) — Final velocity (m/s)
• \( u \) — Initial velocity (m/s)
• \( a \) — Acceleration (m/s²)
• \( s \) — Displacement (m)

Explanation: This equation is particularly useful when time is unknown but displacement and acceleration are known.

3. Importance of Final Velocity Calculation

Details: Calculating final velocity without time is essential in physics problems where time is not given or not measurable, such as in certain kinematic scenarios and engineering applications.

4. Using the Calculator

Tips: Enter initial velocity in m/s, acceleration in m/s², and displacement in meters. Displacement must be non-negative.

5. Frequently Asked Questions (FAQ)

Q1: When should I use this equation?
A: Use this equation when you know initial velocity, acceleration, and displacement, but time is unknown.

Q2: What if acceleration is negative?
A: Negative acceleration (deceleration) is acceptable and will result in a decrease in velocity.

Q3: Can this be used for free fall?
A: Yes, for free fall, set acceleration to 9.8 m/s² (or -9.8 m/s² if upward is positive).

Q4: What are the units for this equation?
A: All inputs should be in SI units: meters for displacement, m/s for velocity, and m/s² for acceleration.

Q5: Is this equation valid for non-constant acceleration?
A: No, this equation assumes constant acceleration. For variable acceleration, integration methods are required.