1. What Is The Final Velocity Formula?

The final velocity formula \( v_f^2 = v_i^2 + 2 a x \) is a fundamental equation in kinematics that relates an object's final velocity to its initial velocity, acceleration, and displacement. It's derived from the equations of motion and is particularly useful when time is not known.

2. How Does The Calculator Work?

The calculator uses the final velocity formula:

Where:

• \( v_f \) — Final velocity (m/s)
• \( v_i \) — Initial velocity (m/s)
• \( a \) — Acceleration (m/s²)
• \( x \) — Displacement (m)

Explanation: This equation calculates the square of the final velocity by adding the square of the initial velocity to twice the product of acceleration and displacement.

3. Applications Of The Formula

Details: This formula is widely used in physics and engineering to solve problems involving motion with constant acceleration, such as calculating stopping distances, projectile motion, and vehicle performance analysis.

4. Using The Calculator

Tips: Enter initial velocity in m/s, acceleration in m/s², and displacement in meters. All values must be valid numerical values.

5. Frequently Asked Questions (FAQ)

Q1: When is this formula applicable?
A: This formula applies only to motion with constant acceleration along a straight line.

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

Q3: Can this formula be used for vertical motion?
A: Yes, when accounting for gravitational acceleration (approximately -9.8 m/s² downward).

Q4: What are the units for each variable?
A: Velocity in m/s, acceleration in m/s², and displacement in meters. Consistent units are essential.

Q5: How is this formula derived?
A: It's derived by eliminating time from the two standard equations: v = u + at and s = ut + ½at².