\(\def \u#1{\,\mathrm{#1}}\) \(\def \abs#1{\left|#1\right|}\) \(\def \ast{*}\) \(\def \deg{^{\circ}}\) \(\def \ten#1{\times 10^{#1}}\) \(\def \redcancel#1{{\color{red}\cancel{#1}}}\) \(\def \BLUE#1{{\color{blue} #1}}\) \(\def \RED#1{{\color{red} #1}}\) \(\def \PURPLE#1{{\color{purple} #1}}\) \(\def \th#1,#2{#1,\!#2}\) \(\def \lshift#1#2{\underset{\Leftarrow\atop{#2}}#1}}\) \(\def \rshift#1#2{\underset{\Rightarrow\atop{#2}}#1}}\) \(\def \dotspot{{\color{lightgray}{\circ}}}\)
Chapter 2: Laws of Motion
1.

Velocity vs Speed

Before we can continue we need to talk about the concept of velocity and its relationship to speed.

Speed
\(v\)
m/s
You already know what speed is. Your car might move at a speed of 25 miles per hour. You probably walk at a speed of 2 or 3 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.

The conversion factor between m/s and miles per hour (as we show in Unit Conversion) is \(1\u{m/s} = 2.2\u{mi/hr}\), so if you're used to American units, you can double the speed in meters per second to get a rough equivalent in miles per hour: e.g.
10m/s ≈ 20mph ≈ 32kph
.

Velocity
\(\vec v\)
m/s

(no alternate text)

Velocity is different from speed in that it includes the direction of motion as well as how fast the motion is. 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.