# An object travels North at 9 m/s for 4 s and then travels South at 3 m/s for  1 s. What are the object's average speed and velocity?

May 9, 2018

$\text{average speed} = 7.8 \frac{m}{s}$ and $\text{average velocity} = 6.6 \frac{m}{s}$

#### Explanation:

While going North, the object goes $9 \frac{m}{\cancel{s}} \cdot 4 \cancel{s} = 36 m$.

While going South, the object goes $3 \frac{m}{\cancel{s}} \cdot 1 \cancel{s} = 3 m$.

For average speed , direction does not matter, just total distance and total time.

$\text{average speed" = "total distance"/"total time} = \frac{36 m + 3 m}{4 s + 1 s} = 7.8 \frac{m}{s}$

For average velocity, direction does matter, so we need the resultant of all displacements (which are vectors) and total time.

$\text{average velocity" = "net displacement"/"total time} = \frac{36 m - 3 m}{4 s + 1 s} = 6.6 \frac{m}{s}$ to the North.

I hope this helps,
Steve