velocity (one-dimensional)

Velocity is the time rate of change of position. Velocity is a vector, and so has magnitude and direction. For one-dimensional motion, the direction is often specified by the mathematical sign of the velocity. A positive velocity indicates motion in one (arbitrarily chosen) direction, while a negative velocity indicates the opposite direction.

Representations

1. Differential

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2. Integral

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   +2\int_{x_{\rm i}}^{x_{\rm f}}a\:dx$\end

3. Graphical

   Besides explicit velocity graphs, velocity can be found from the slope of a distance vs. time graph or (if the initial velocity is known) by adding the area under an acceleration vs. time graph to the initial velocity.

4. Through Motion Diagrams

   In a motion diagram, the velocity can be estimated by looking at the spacing of the individual snapshots (assuming that the snapshots are separated by equal time intervals).

Relevant Models

• One-Dimensional Motion (General)
  • 1-D Motion (Constant Acceleration)
    • 1-D Motion (Constant Velocity)
  • Simple Harmonic Motion
• Rotational Motion
  • Uniform Circular Motion

Relevant Examples