# Speed

## Definition

Speed is the scalar quantity of change in distance travelled along a path, divided by the time it takes to travel that part of the path.

## Contrast with velocity

Speed is different from velocity, the latter has direction. Here's why that changes things: $A\\\rule{0.513\textwidth}{1pt}\\[-1.5pt]\ignorespaces\rule{1pt}{1cm}\rule{1cm}{1pt}\rule{1pt}{1cm}\rule{1cm}{1pt}\rule{1pt}{1cm}\rule{1cm}{1pt}\rule{1pt}{1cm}\rule{1cm}{1pt}\rule{1pt}{1cm}\rule{1cm}{1pt}\rule{1pt}{1cm}\\\rule{0.513\textwidth}{0pt}B$

Say $A$ wanted to get to $B$, if $A$ can only travel the paths drawn, $A$ would have to go 6 units of length (be they metres,kilometres, miles, yards,etc.). If they take 6 minutes then they averaged 1 unit of length per minute, this is their average speed (usually taken to just be speed).

On the other hand, velocity depends on a distance (called displacement) and 'direction. If A walks around the block (4 equal sides), she may have walked 4 units of length in 4 minutes; giving her a speed of 1 unit of length per minute. However she has a distance from point of origin (called displacement) of 0 units of length; therefore her velocity is 0 units of length per minute in the opposite path direction to which she arrived back at the point of origin.