1. What is the Distance Equation?

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

2. How Does the Calculator Work?

The calculator uses the distance equation:

Where:

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

Explanation: This equation calculates the total distance traveled by summing the distance covered due to initial velocity and the additional distance from constant acceleration over time.

3. Importance of Distance Calculation

Details: Accurate distance calculation is crucial for physics problems, engineering applications, motion analysis, and understanding object movement under various acceleration conditions.

4. Using the Calculator

Tips: Enter initial velocity in m/s, acceleration in m/s², and time in seconds. Time must be non-negative. All values should be valid numbers.

5. Frequently Asked Questions (FAQ)

Q1: What if acceleration is zero?
A: If acceleration is zero, the equation simplifies to \( d = u t \), representing constant velocity motion.

Q2: Can this equation be used for deceleration?
A: Yes, deceleration is simply negative acceleration. Use a negative value for acceleration when the object is slowing down.

Q3: What are the SI units for this equation?
A: The standard units are meters for distance, m/s for velocity, m/s² for acceleration, and seconds for time.

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

Q5: What if initial velocity is zero?
A: If initial velocity is zero, the equation simplifies to \( d = \frac{1}{2} a t^2 \), representing motion starting from rest under constant acceleration.