1. What is the Distance Equation?

The distance equation \( d = \frac{v^2 - u^2}{2a} \) calculates the distance traveled by an object under constant acceleration, given its initial velocity, final velocity, and acceleration. This equation is derived from the equations of motion in physics.

2. How Does the Calculator Work?

The calculator uses the distance equation:

Where:

• \( d \) — Distance traveled (meters)
• \( v \) — Final velocity (m/s)
• \( u \) — Initial velocity (m/s)
• \( a \) — Acceleration (m/s²)

Explanation: This equation calculates the distance an object travels when accelerating from initial velocity u to final velocity v with constant acceleration a.

3. Applications of Distance Calculation

Details: This calculation is essential in physics, engineering, and transportation planning. It helps determine stopping distances for vehicles, projectile motion analysis, and various mechanical system designs.

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 as it would result in division by zero.

5. Frequently Asked Questions (FAQ)

Q1: What if acceleration is negative?
A: Negative acceleration (deceleration) is acceptable and will result in a positive distance value as long as the numerator (v² - u²) is also negative.

Q2: Can this equation be used for non-constant acceleration?
A: No, this equation assumes constant acceleration. For variable acceleration, integration methods are required.

Q3: What are typical units for this calculation?
A: The standard SI units are meters for distance, m/s for velocity, and m/s² for acceleration.

Q4: When is this equation not applicable?
A: This equation is not applicable when acceleration is not constant, or when dealing with relativistic speeds where classical mechanics breaks down.

Q5: How is this equation derived?
A: This equation is derived by eliminating time from the two standard equations of motion: v = u + at and s = ut + ½at².