1. What Is The Initial Velocity Given Displacement, Uniform Acceleration And Final Velocity Of Particle Formula?

This formula calculates the initial velocity of a particle undergoing uniformly accelerated linear motion, given its final velocity, acceleration, and displacement. It's derived from the standard equations of motion.

2. How Does The Calculator Work?

The calculator uses the formula:

Where:

• \( u \) — Initial velocity (m/s)
• \( v_f \) — Final velocity (m/s)
• \( a_{lm} \) — Acceleration for linear motion (m/s²)
• \( d \) — Displacement (m)

Explanation: This formula is derived from the kinematic equation \( v_f^2 = u^2 + 2ad \), rearranged to solve for initial velocity \( u \).

3. Importance Of Initial Velocity Calculation

Details: Calculating initial velocity is essential in physics and engineering for analyzing motion, predicting trajectories, and understanding the behavior of moving objects under constant acceleration.

4. Using The Calculator

Tips: Enter final velocity in m/s, acceleration in m/s², and displacement in meters. All values must be valid (non-negative for velocity and displacement).

5. Frequently Asked Questions (FAQ)

Q1: What if the value under the square root is negative?
A: A negative value indicates that the given combination of parameters is not physically possible for real motion.

Q2: Does this formula work for deceleration?
A: Yes, acceleration can be negative (deceleration) in this formula.

Q3: What are the units for each variable?
A: All velocities are in m/s, acceleration in m/s², and displacement in meters.

Q4: Can this be used for non-uniform acceleration?
A: No, this formula only applies to motion with constant (uniform) acceleration.

Q5: What's the difference between velocity and speed?
A: Velocity is a vector quantity (magnitude and direction), while speed is a scalar (magnitude only). This formula calculates velocity.