1. What is the Distance Formula?

The distance formula \( d = v_i t + 0.5 a t^2 \) calculates the distance traveled by an object under constant acceleration, where \( v_i \) is the initial velocity, \( a \) is the acceleration, and \( t \) is the time elapsed.

2. How Does the Calculator Work?

The calculator uses the distance formula:

Where:

• \( d \) — Distance traveled (meters)
• \( v_i \) — Initial velocity (m/s)
• \( t \) — Time elapsed (seconds)
• \( a \) — Constant acceleration (m/s²)

Explanation: This equation combines the distance covered due to initial velocity and the additional distance covered due to constant acceleration over time.

3. Applications of Distance Calculation

Details: This formula is fundamental in physics for analyzing motion under constant acceleration, with applications in vehicle braking distance calculation, projectile motion analysis, and engineering design.

4. Using the Calculator

Tips: Enter initial velocity in m/s, time in seconds, and acceleration in m/s². Time must be a positive value. All values can be positive or negative depending on direction.

5. Frequently Asked Questions (FAQ)

Q1: What if acceleration is zero?
A: If acceleration is zero, the formula simplifies to \( d = v_i t \), representing uniform motion without acceleration.

Q2: Can this formula be used for deceleration?
A: Yes, deceleration is simply negative acceleration. Enter a negative value for acceleration when an object is slowing down.

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

Q4: Does this formula work for variable acceleration?
A: No, this formula only applies when acceleration is constant. For variable acceleration, calculus-based methods are required.

Q5: How is this formula derived?
A: The formula is derived by integrating the velocity equation with respect to time, assuming constant acceleration.