Defnition
The time rate of change of position. Velocity is a vector quantity. 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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Representations
Differential
\begin
$v = \frac
$\end
Integral
\begin
$v = v_
+\int_{t_{\rm i}}^
a\:dt$\end
\begin
$v^
=v_
^
+2\int_{x_{\rm i}}^
a\:dx$\end
Graphical
Besides explicit velocity graphs, velocity can be found from the slope of a position vs. time graph or (if the initial velocity is known) by adding the area under an acceleration vs. time graph to the initial velocity.
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).