1. What is the Distance Equation?

The distance equation calculates the displacement of an object under constant acceleration. It is derived from the equations of motion and is fundamental in classical mechanics for analyzing object movement.

2. How Does the Calculator Work?

The calculator uses the distance equation:

Where:

• \( d \) — Distance traveled (meters)
• \( v_i \) — Initial velocity (meters/second)
• \( a \) — Acceleration (meters/second²)
• \( t \) — Time (seconds)

Explanation: The equation combines the distance covered due to initial velocity with the additional distance gained (or lost) due to constant acceleration over time.

3. Importance of Distance Calculation

Details: This calculation is essential in physics, engineering, and motion analysis for predicting object positions, designing transportation systems, and solving real-world motion problems.

4. Using the Calculator

Tips: Enter initial velocity in m/s, acceleration in m/s², and time in seconds. Time must be positive. Negative acceleration indicates deceleration.

5. Frequently Asked Questions (FAQ)

Q1: What if initial velocity is zero?
A: The equation simplifies to \( d = \frac{1}{2} a t^2 \), which describes distance covered from rest under constant acceleration.

Q2: Can this be used for free fall?
A: Yes, for free fall near Earth's surface, use \( a = -9.8 \, m/s^2 \) (downward direction) and appropriate initial velocity.

Q3: What are the units for each variable?
A: Distance in meters (m), initial velocity in m/s, acceleration in m/s², and time in seconds (s).

Q4: Does this work for non-constant acceleration?
A: No, this equation assumes constant acceleration. For variable acceleration, integration methods are required.

Q5: What does negative distance indicate?
A: Negative distance typically indicates displacement in the opposite direction of the chosen positive coordinate system.