# An object travels North at 2 m/s for 8 s and then travels South at 3 m/s for  2 s. What are the object's average speed and velocity?

Jun 10, 2016

Average speed: $2.2 \frac{m}{s} \textcolor{w h i t e}{\text{XXXX}}$Average velocity: $1 \frac{m}{s} \text{North}$

#### Explanation:

$\text{Distance traveled}$
color(white)("XXX")="Distance traveled going North"+"Distance traveled going South"

$\textcolor{w h i t e}{\text{XXX}} = 2 \frac{m}{s} \times 8 s + 3 \frac{m}{s} \times 2 s$

$\textcolor{w h i t e}{\text{XXX}} = 16 m + 6 m$

$\textcolor{w h i t e}{\text{XXX}} = 22 m$

$\text{Duration of travel}$
color(white)("XXX")"Time traveling North" + "Time traveling South"

$\textcolor{w h i t e}{\text{XXX}} = 8 s + 2 s$

$\textcolor{w h i t e}{\text{XXX}} = 10 s$

$\textcolor{red}{\text{Average speed}}$
color(white)("XXX")="Distance traveled"/"Duration of travel"

$\textcolor{w h i t e}{\text{XXX}} = \frac{22 m}{10 s}$

$\textcolor{w h i t e}{\text{XXX}} = 2.2 \frac{m}{s}$

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Displacement traveled (North)
color(white)("XXX")="Distance traveled North" - "Distance traveled South"

$\textcolor{w h i t e}{\text{XXX}} = 16 m - 6 m$

$\textcolor{w h i t e}{\text{XXX}} = 10 m$

$\textcolor{red}{\text{Average velocity (North)}}$
color(white)("XXX")=("Displacement (North)")/"Duration of travel"

$\frac{\textcolor{w h i t e}{\text{XXX")=(10 m " North}}}{10 s}$

color(white)("XXX")=1m/s " North"