# An object travels North at 8 m/s for 4 s and then travels South at 6 m/s for 7 s. What are the object's average speed and velocity?

Aug 28, 2017

Average speed: $6 \frac{8}{11} \frac{m}{s}$

Average velocity: $\frac{10}{11} \frac{m}{s} \text{ South}$

#### Explanation:

{: (,ul("Distance"),color(white)("xxx"),ul("Displacement")), ("first 4 seconds",8m/sxx4s=32m,,8m/s N xx4s =32 m N), ("second 7 seconds",6m/sxx7s=42m,,6m/s Sxx7s=42 m S) :}
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Total time: $4 s + 7 s = 11 s$

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Total distance: $= 32 m + 42 m = 74 m$

Average speed: $\text{distance"/"time} = \frac{74 m}{11 s} = 6 \frac{8}{11} \frac{m}{s}$

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Total displacement: $32 m \textcolor{red}{N} + 42 m S$
$\textcolor{w h i t e}{\text{XXXXXXXXXXXXXXXXXX}} = \textcolor{red}{-} 32 m \textcolor{red}{S} + 42 m S$
$\textcolor{w h i t e}{\text{XXXXXXXXXXXXXXXXXX}} = 10 m S$

Average velocity: $\text{displacement"/"time} = \frac{10 m S}{11 s} = \frac{10}{11} \frac{m}{s} S$