1. What is the Distance Equation?

The distance equation \( s = v t + \frac{1}{2} a t^2 \) calculates the displacement of an object under constant acceleration. This fundamental physics equation describes motion in a straight line with uniform acceleration.

2. How Does the Calculator Work?

The calculator uses the distance equation:

Where:

• \( s \) — Distance/displacement (meters)
• \( v \) — Initial velocity (meters/second)
• \( t \) — Time (seconds)
• \( a \) — Acceleration (meters/second²)

Explanation: The equation combines the distance traveled due to initial velocity (v*t) with the distance gained from acceleration (½*a*t²).

3. Importance of Distance Calculation

Details: This calculation is essential in physics, engineering, and motion analysis for predicting object positions, designing transportation systems, and analyzing projectile motion.

4. Using the Calculator

Tips: Enter initial velocity in m/s, time in seconds, and acceleration in m/s². 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 \( s = \frac{1}{2} a t^2 \), which describes motion starting 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/s² (negative for downward direction).

Q3: What are the units for each variable?
A: Distance (m), velocity (m/s), time (s), acceleration (m/s²). Ensure consistent units for accurate results.

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

Q5: What's the difference between distance and displacement?
A: Distance is total path length, while displacement is straight-line distance from start to end point. This equation calculates displacement.