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  • Velocity Equations: Derivation & Common Formulas
    The derived equation of velocity depends on what information you have and what you're trying to find. Here are the most common scenarios:

    1. From initial velocity, acceleration, and time:

    * Equation: v = u + at

    * v: Final velocity

    * u: Initial velocity

    * a: Acceleration

    * t: Time

    2. From displacement, initial velocity, and time:

    * Equation: v = (s - ut) / t

    * v: Final velocity

    * s: Displacement

    * u: Initial velocity

    * t: Time

    3. From displacement, acceleration, and initial velocity:

    * Equation: v² = u² + 2as

    * v: Final velocity

    * u: Initial velocity

    * a: Acceleration

    * s: Displacement

    4. From average velocity and time:

    * Equation: v = (Δx) / Δt

    * v: Average velocity

    * Δx: Change in position (displacement)

    * Δt: Change in time

    Important Notes:

    * Constant acceleration: These equations assume constant acceleration.

    * Vectors: Velocity is a vector quantity (it has both magnitude and direction). The equations above are typically used for the magnitude of velocity.

    * Units: Make sure to use consistent units for all quantities in the equations.

    Let me know if you have a specific scenario in mind, and I can help you derive the appropriate velocity equation!

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