1. What is the Displacement Equation?

The displacement equation s = ut + (1/2)at² calculates the displacement of an object under constant acceleration. It's one of the fundamental equations of motion in physics, relating initial velocity, acceleration, time, and displacement.

2. How Does the Calculator Work?

The calculator uses the displacement equation:

Where:

• \( s \) — Displacement (m)
• \( u \) — Initial velocity (m/s)
• \( a \) — Acceleration (m/s²)
• \( t \) — Time (s)

Explanation: The equation calculates how far an object has traveled given its starting speed, constant acceleration, and time elapsed.

3. Importance of Displacement Calculation

Details: Calculating displacement is essential in physics and engineering for understanding motion, predicting positions, and solving kinematics problems. It's fundamental to mechanics and motion analysis.

4. Using the Calculator

Tips: Enter initial velocity in m/s, acceleration in m/s², and time in seconds. Time must be a non-negative value. All values can be positive, negative, or zero depending on the direction of motion.

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 traveled.

Q2: Can acceleration be negative in this equation?
A: Yes, negative acceleration (deceleration) will result in less displacement or even negative displacement if the object changes direction.

Q3: What if initial velocity is zero?
A: If u = 0, the equation simplifies to s = (1/2)at², which describes displacement under constant acceleration from rest.

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

Q5: What are typical units for this equation?
A: The SI units are meters (m) for displacement, meters per second (m/s) for velocity, meters per second squared (m/s²) for acceleration, and seconds (s) for time.