1. What is the Distance Equation?

The distance equation \( d = v_i t + \frac{1}{2} a t^2 \) calculates the distance traveled by an object under constant acceleration. It's a fundamental equation in kinematics that relates initial velocity, time, acceleration, and displacement.

2. How Does the Calculator Work?

The calculator uses the distance equation:

Where:

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

Explanation: The equation accounts for both the distance covered due to initial velocity and the additional distance from constant acceleration over time.

3. Importance of Distance Calculation

Details: This calculation is essential in physics, engineering, and motion analysis. It helps predict object position, plan trajectories, and understand motion dynamics in various applications from vehicle braking to 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. All values can be positive, negative, or zero depending on the direction of motion.

5. Frequently Asked Questions (FAQ)

Q1: What does negative acceleration mean?
A: Negative acceleration (deceleration) means the object is slowing down. The distance calculation will account for this reduction in speed over time.

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

Q3: What if acceleration is zero?
A: With zero acceleration, the equation simplifies to \( d = v_i t \), representing constant velocity motion.

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

Q5: What are the limitations of this equation?
A: This equation assumes constant acceleration. It doesn't account for air resistance, changing forces, or non-uniform acceleration scenarios.