# An object travels North at  2 m/s for 1 s and then travels South at  4 m/s for  9 s. What are the object's average speed and velocity?

Jun 26, 2017

Average velocity = $\text{-"3.09..."ms"^-1 "south}$
Average speed = $3.45 \ldots {\text{ms}}^{-} 1$

#### Explanation:

We will deal with speed first. Speed is how far something travels per second.

North - $\text{speed"*"time"="distance"; 2*1=2"m}$
South - $\text{speed"*"time"="distance"; 4*9=36"m}$

Total distance travelled = 2+36=38m
Total time = 2 + 9 = 11s

$\text{Average speed" = "total distamce"/"total time}$

${\text{Average speed" = 38/11 = 3.45..."ms}}^{-} 1$

Average velocity:

As average takes direction into accpunt as well, the north value will be taken as positive, and the south value as negative (opposite directions, think add and subtract).

North - $\text{velocity"*"time"="displacement"; 2*1=2"m}$
South - $\text{velocity"*"time"="displacement"; "-"4*9="-"36"m}$

Total displacement = 2-36=-34m
Total time = 2 + 9 = 11s

$\text{Average velocity" = "total displacement"/"total time}$

${\text{Average velocity" = "-"34/11 = -3.09..."ms}}^{-} 1$

As the value for average velocity is negative, and so is the inital south value, the average velocity is therefore $\text{-"3.09..."ms"^-1 "south}$.