1. What is the Distance Formula?

The distance formula \( d = \frac{v_f^2 - v_i^2}{2a} \) calculates the distance traveled by an object under constant acceleration, using initial and final velocities. This equation is derived from the kinematic equations of motion.

2. How Does the Calculator Work?

The calculator uses the distance formula:

Where:

• \( d \) — Distance traveled (meters)
• \( v_f \) — Final velocity (m/s)
• \( v_i \) — Initial velocity (m/s)
• \( a \) — Constant acceleration (m/s²)

Explanation: This formula calculates the distance an object travels when accelerating from initial velocity to final velocity at a constant rate.

3. Importance of Distance Calculation

Details: Accurate distance calculation is crucial for physics problems, engineering applications, motion analysis, and understanding kinematics in various scientific contexts.

4. Using the Calculator

Tips: Enter final velocity in m/s, initial velocity in m/s, and acceleration in m/s². Acceleration cannot be zero. All values must be valid numerical values.

5. Frequently Asked Questions (FAQ)

Q1: What if acceleration is zero?
A: The formula cannot be used when acceleration is zero as it would result in division by zero. For zero acceleration, use d = v × t.

Q2: Can this formula be used for deceleration?
A: Yes, deceleration is simply negative acceleration. The formula works the same way with negative acceleration values.

Q3: What are the units for this calculation?
A: The formula uses SI units: meters for distance, meters per second for velocity, and meters per second squared for acceleration.

Q4: When is this formula applicable?
A: This formula applies only when acceleration is constant. For variable acceleration, integration methods must be used.

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