1. What is the Distance Equation?

The distance equation \( s = u t + \frac{1}{2} a t^2 \) calculates the distance traveled by an object under constant acceleration. This fundamental physics equation is essential for analyzing motion in kinematics.

2. How Does the Calculator Work?

The calculator uses the distance equation:

Where:

• \( s \) — Distance traveled (meters)
• \( u \) — Initial velocity (meters per second)
• \( t \) — Time elapsed (seconds)
• \( a \) — Constant acceleration (meters per second squared)

Explanation: The equation combines the distance covered due to initial velocity (ut) with the distance covered due to acceleration (½at²) to give total displacement.

3. Importance of Distance Calculation

Details: This calculation is crucial 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, time in seconds, and acceleration in m/s². Time must be positive. All values can be positive, negative, or zero depending on the motion scenario.

5. Frequently Asked Questions (FAQ)

Q1: What does negative acceleration mean?
A: Negative acceleration indicates deceleration or acceleration in the opposite direction to the initial velocity.

Q2: Can initial velocity be zero?
A: Yes, if an object starts from rest, initial velocity is zero and the equation simplifies to \( s = \frac{1}{2} a t^2 \).

Q3: What if acceleration is zero?
A: With zero acceleration, the object moves with constant velocity and the equation becomes \( s = u t \).

Q4: Does this work for vertical motion?
A: Yes, for vertical motion under gravity, use \( a = -9.8 \, m/s^2 \) (downward direction).

Q5: What are the units of measurement?
A: Use consistent SI units: meters for distance, meters/second for velocity, seconds for time, and meters/second² for acceleration.