# An object travels North at 2 m/s for 9 s and then travels South at 4 m/s for 5 s. What are the object's average speed and velocity?

May 7, 2016

$\text{displacement=} - 2 m$
$\text{velocity=} - \frac{1}{7} \frac{m}{s}$
$\text{speed=} \frac{19}{7} \frac{m}{s}$

#### Explanation:

$\text{displacement to the north direction: } v \cdot t = 2 \cdot 9 = 18 m$
$\text{displacement to the south direction:} v \cdot t = 4 \cdot 5 = 20 m$

$\text{displacement=} - 2 m$

$\text{velocity"=("displacement")/"time}$

"velocity=(-2)/(9+5)

$\text{velocity=} - \frac{2}{14}$

$\text{velocity=} - \frac{1}{7} \frac{m}{s}$

"speed="("distance")/("time")

$\text{speed=} \frac{2 \cdot 9 + 4 \cdot 5}{9 + 5}$

$\text{speed=} \frac{18 + 20}{14}$

$\text{speed=} \frac{38}{14}$

$\text{speed=} \frac{19}{7} \frac{m}{s}$