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Velocity (a vector) 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.
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h2. Representations

h4. Differential 
  {latex}\begin{Large} $v = \frac{dx}{dt}$\end{Large}{latex}
h4. Integral
 {latex}\begin{Large} $v_{\rm f} = v_{\rm i}+\int_{t_{\rm i}}^{t_{\rm f}}a\:dt$\end{Large}{latex}\\
{latex}\begin{Large}$v_{\rm f}^{2}=v_{\rm i}^{2}+2\int_{x_{\rm i}}^{x_{\rm f}}a\:dx$\end{Large}{latex}
h4. 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.
h4. 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).

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h2. Relevant Models

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h2. Relevant Examples

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