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Displacement Equation:
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The displacement equation \( s = u t + \frac{1}{2} a t^2 \) calculates the distance traveled by an object under constant acceleration. It is one of the fundamental equations of motion in classical mechanics.
The calculator uses the displacement equation:
Where:
Explanation: This equation combines the distance covered due to initial velocity (ut) with the distance covered due to acceleration (½at²) to give total displacement.
Details: Accurate displacement calculation is crucial for analyzing motion in physics, engineering applications, vehicle dynamics, projectile motion, and understanding kinematic relationships.
Tips: Enter initial velocity in m/s, time in seconds, and acceleration in m/s². Time must be positive. All values can be positive, negative, or zero depending on the motion direction.
Q1: What is the difference between distance and displacement?
A: Distance is the total path length traveled, while displacement is the straight-line distance from start to finish point with direction.
Q2: Can acceleration be negative in this equation?
A: Yes, negative acceleration (deceleration) will reduce the displacement. The equation works for both positive and negative acceleration values.
Q3: What happens if initial velocity is zero?
A: If u = 0, the equation simplifies to s = ½at², representing motion starting from rest under constant acceleration.
Q4: Is this equation valid for all types of motion?
A: This equation is valid only for motion with constant acceleration. For variable acceleration, calculus-based methods are required.
Q5: How does this relate to other equations of motion?
A: This is one of the four standard kinematic equations. The others include v = u + at, v² = u² + 2as, and s = (u+v)t/2.