1. What is the Displacement Equation?

The displacement equation \( s = ut + \frac{1}{2}at^2 \) is a fundamental equation of motion in physics that calculates the displacement of an object under constant acceleration. It takes into account the initial velocity, time, and acceleration of the object.

2. How Does the Calculator Work?

The calculator uses the displacement equation:

Where:

• \( s \) — Displacement (meters)
• \( u \) — Initial velocity (meters/second)
• \( t \) — Time (seconds)
• \( a \) — Acceleration (meters/second²)

Explanation: The equation calculates how far an object travels considering both its initial speed and any acceleration over time.

3. Importance of Displacement Calculation

Details: Displacement is crucial in physics for understanding motion, predicting object positions, and solving problems related to kinematics and dynamics.

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 displacement be negative?
A: Yes, negative displacement indicates movement in the opposite direction from the reference point.

Q3: What if acceleration is zero?
A: The equation simplifies to \( s = ut \), representing uniform motion with constant velocity.

Q4: How does this relate to free-fall motion?
A: For free-fall near Earth's surface, acceleration \( a \) would be -9.81 m/s² (negative for upward positive convention).

Q5: What are the limitations of this equation?
A: It only works for constant acceleration. For variable acceleration, calculus-based methods are needed.