1. What is the Distance Equation?

The distance equation \( d = \frac{1}{2} a t^2 \) calculates the distance traveled by an object under constant acceleration, starting from rest. This fundamental physics equation is derived from kinematic equations of motion.

2. How Does the Calculator Work?

The calculator uses the distance equation:

Where:

• \( d \) — Distance traveled (meters)
• \( a \) — Constant acceleration (m/s²)
• \( t \) — Time elapsed (seconds)

Explanation: The equation assumes the object starts from rest (initial velocity = 0) and experiences constant acceleration throughout the motion.

3. Importance of Distance Calculation

Details: This calculation is essential in physics, engineering, and various real-world applications including vehicle braking distance, projectile motion, and mechanical system design.

4. Using the Calculator

Tips: Enter acceleration in m/s² and time in seconds. Both values must be positive numbers greater than zero for valid calculations.

5. Frequently Asked Questions (FAQ)

Q1: What if the object doesn't start from rest?
A: For objects with initial velocity, use the equation \( d = v_0 t + \frac{1}{2} a t^2 \), where \( v_0 \) is the initial velocity.

Q2: Does this equation work for deceleration?
A: Yes, use a negative acceleration value for deceleration (slowing down).

Q3: What are typical acceleration values?
A: Earth's gravity is approximately 9.8 m/s². Car acceleration ranges from 2-4 m/s², while braking deceleration can be 6-8 m/s².

Q4: Are there limitations to this equation?
A: This equation assumes constant acceleration and no air resistance. It's less accurate for objects experiencing variable acceleration.

Q5: How is this equation derived?
A: It's derived by integrating the acceleration function twice with respect to time, assuming constant acceleration and zero initial velocity.