# An object travels North at  7 m/s for 6 s and then travels South at  3 m/s for  3 s. What are the object's average speed and velocity?

Oct 8, 2016

$\textcolor{g r e e n}{\text{Average speed: "5 2/3 " m/s}}$

$\textcolor{b l u e}{\text{Average velocity: "3 2/3 " m/s North}}$

#### Explanation:

Distance:
$\textcolor{w h i t e}{\text{X}}$First $6 s$: $\textcolor{w h i t e}{\text{XX}} 7 \frac{m}{s} \cdot 6 s = 42 m$
$\textcolor{w h i t e}{\text{X}}$Last $3 x$: $\textcolor{w h i t e}{\text{XX}} 3 \frac{m}{s} \cdot 3 s = 9 m$
Total distance traveled: $42 m + 9 m = 51 m$
over a period of $6 s + 3 s = 9 s$
for an average speed of $\frac{51}{9} \frac{m}{s} = 5 \frac{2}{3} \frac{m}{s}$

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Displacement:
$\textcolor{w h i t e}{\text{X}}$First $6 s$: $\textcolor{w h i t e}{\text{XX}} 7 \frac{m}{s} N \cdot 6 s = 42 m N$
$\textcolor{w h i t e}{\text{X}}$Last $3 s$: $\textcolor{w h i t e}{\text{XX}} 3 \frac{m}{s} S \cdot 3 s = 9 m S = - 9 m N$
Total displacement traveled: $42 m N + \left(- 9\right) m N = 33 m N$
over a period of $6 s + 3 s = 9 s$
for an average velocity of $\frac{33}{9} \frac{m}{s} N = 3 \frac{2}{3} \frac{m}{s} N$