1. What is the Displacement Equation?

The displacement equation \( s = ut + \frac{1}{2}at^2 \) is a fundamental equation in one-dimensional kinematics that calculates the displacement of an object under constant acceleration. It relates displacement to initial velocity, time, and acceleration.

2. How Does the Calculator Work?

The calculator uses the displacement equation:

Where:

• \( s \) — Displacement (meters)
• \( u \) — Initial velocity (m/s)
• \( t \) — Time (seconds)
• \( a \) — Constant acceleration (m/s²)

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

3. Importance of Displacement Calculation

Details: Calculating displacement is crucial in physics for determining an object's position change, analyzing motion, and solving problems in mechanics and engineering.

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 or negative depending on direction.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between displacement and distance?
A: Displacement is a vector quantity (magnitude and direction) measuring change in position, while distance is a scalar quantity measuring total path length.

Q2: Can this equation be used for non-constant acceleration?
A: No, this equation only works for constant acceleration. For variable acceleration, calculus-based methods are needed.

Q3: What does negative displacement mean?
A: Negative displacement indicates motion in the opposite direction of your chosen positive reference direction.

Q4: How does initial velocity affect displacement?
A: Higher initial velocity increases the linear term in the equation, directly proportional to time.

Q5: What's the significance of the ½ in the equation?
A: The ½ comes from integrating acceleration over time, representing how displacement increases quadratically with time under constant acceleration.