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Velocity Calculator

Calculate average velocity ($v$), displacement ($\Delta d$), time ($\Delta t$), or final velocity ($v_f$).

Average Velocity from Displacement ($v = \frac{\Delta d}{\Delta t}$)

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Final Velocity from Acceleration ($v_f = v_i + a \Delta t$)

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What is Velocity?

In physics, velocity ($v$) is the rate at which an object changes its position. It's often confused with speed, but they are not the same. Speed is a scalar quantity (it only has magnitude, like 60 mph). Velocity is a vector quantity, meaning it has both magnitude and direction (e.g., 60 mph *north*).

An object's velocity can change in three ways:

  • Its speed changes (it speeds up).
  • Its speed changes (it slows down).
  • Its direction of motion changes (like a car turning a corner).
Any of these changes constitutes an acceleration. Velocity is typically measured in meters per second (m/s).

The Velocity Formulas

1. Average Velocity from Displacement and Time

The most fundamental definition of average velocity is the total displacement (change in position) divided by the total time taken for that displacement.

  • $v_{avg}$: Average velocity, measured in meters per second (m/s).
  • $\Delta d$: Displacement (change in position), measured in meters (m).
  • $\Delta t$: The time interval, measured in seconds (s).

2. Final Velocity from Acceleration and Time

If an object is undergoing constant acceleration, its final velocity can be found using one of the key kinematic equations. This formula calculates the final velocity based on its initial velocity, its acceleration, and the time it was accelerating.

  • $v_f$: Final velocity, in meters per second (m/s).
  • $v_i$: Initial velocity, in meters per second (m/s).
  • $a$: Acceleration, measured in m/s².
  • $\Delta t$: The time interval, in seconds (s).

Related Concepts

  • Acceleration: Acceleration is the *rate of change* of velocity. If velocity is constant, acceleration is zero. If velocity is changing (speeding up, slowing down, or turning), the object is accelerating.
  • Momentum: Velocity is a core component of momentum ($p = mv$). An object's momentum is its mass multiplied by its velocity. If you change an object's velocity, you change its momentum.
  • Impulse: An impulse (a force applied over time) is what *causes* a change in velocity. The impulse-momentum theorem ($F \Delta t = m \Delta v$) directly links force to the change in velocity.