Velocity vs Speed

So far we've only talked about systems in static equilibrium, where nothing is moving. Now we want to talk about motion, but before we can continue we need to define the concept of velocity and the related concept speed.

Speed

$v$

Units:m/s

Typical Speeds	m/s
Walking	1
Residential driving	10
Highway driving	30
Airplane	250

1m/s = 2.2mph

1m/s = 3.6km/hr

You already know what speed is; the distance something travels divided by the time it took to travel. In everyday life we usually measure this in km/hr or miles per hour. The SI unit for speed is meters per second, written m/s; one meter per second is roughly how fast a person walks. Note that speed is never negative.

Velocity

$\vec v$

Units:m/s

Velocity, on the other hand, is a vector quantity, and so includes the direction. of motion as well. So "20 m/s to the right" is a velocity, but "20m/s" is the speed associated with that velocity. Graphically, we can represent a velocity by drawing an arrow in the direction of motion and labelling it with the corresponding speed.

If an object isn't moving at all we say it has "zero velocity", and we don't bother indicating a direction.

Note

As a quick approximation, you can double the speed in m/s to get the speed in mph, and you can double it again to get the speed in km/hr. So $10\u{m/s}$ is roughly $20\u{mph}$ or $40\u{km/hr}$. This may be useful in developing your intuition for the SI unit.