# An object travels North at 6 m/s for 3 s and then travels South at 5 m/s for  7 s. What are the object's average speed and velocity?

May 20, 2017

Average speed is $5.3 \frac{m}{s}$.

Average velocity is $1.7 \frac{m}{s} \text{ South}$.

#### Explanation:

$\text{Average speed" = "Distance"/"Time}$

The total distance is $6 \frac{m}{s} \cdot 3 s + 5 \frac{m}{s} \cdot 7 s = 18 m + 35 m = 53 m$.

The total time is $3 s + 7 s = 10 s$.

Therefore the average speed is $\frac{53 m}{10 s} = 5.3 \frac{m}{s}$.

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$\text{Average velocity" = "Displacement"/"Time}$

The total displacement is :

$18 m \text{ North" + 35m " South" = 17m " South}$

The total time is $3 s + 7 s = 10 s$.

Therefore the average velocity is (17m " South")/(10s) = 1.7 m/s " South"

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Note that the average speed has no direction while the average velocity does (South).