\(\def \u#1{\,\mathrm{#1}}\) \(\def \abs#1{\left|#1\right|}\) \(\def \ast{*}\) \(\def \deg{^{\circ}}\) \(\def \tau{\uptau}\) \(\def \ten#1{\times 10^{#1}}\) \(\def \redcancel#1{{\color{red}\cancel{#1}}}\) \(\def \BLUE#1{{\color{blue} #1}}\) \(\def \RED#1{{\color{red} #1}}\) \(\def \PURPLE#1{{\color{purple} #1}}\) \(\def \th#1,#2{#1,\!#2}\) \(\def \lshift#1#2{\underset{\Leftarrow\atop{#2}}#1}}\) \(\def \rshift#1#2{\underset{\Rightarrow\atop{#2}}#1}}\) \(\def \dotspot{{\color{lightgray}{\circ}}}\) \(\def \ccw{\circlearrowleft}\) \(\def \cw{\circlearrowright}\)
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

Typical Speedsm/s
Walking1
Residential driving10
Highway driving30
Airplane250

$1\u{m/s} =2.2\u{mph}$ $1\u{m/s} =3.6\u{km/hr}$

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
\(\vec v\)
m/s

We'll use a dotted arrow in this book for velocity vectors, to distinguish it from force.

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 an 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.