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

Nov 13, 2017

Average speed: 6.375 m/s
Average velocity: 1.125 m/s

#### Explanation:

Speed is a scalar quantity (not a vector), and therefore has no direction. Hence, you can just find the average speed by taking total distance travelled and dividing by total time travelled:

"Speed"_(avg) = ("speed"_1 * "time"_1 + "speed"_2 * "time"_2)/("total time") = (5(6) + 3(7))/8 = 6.375 m/s

Velocity, however, is a vector, and therefore you'll need to take into consideration the direction you're running in.

You have to choose whether one of your directions to be the "positive" direction. I'll choose North as the positive direction, so we'll have:

$v = \frac{{v}_{1} \left({t}_{1}\right) \textcolor{red}{-} {v}_{2} \left({t}_{2}\right)}{\text{total time}} = \frac{5 \left(6\right) - 3 \left(7\right)}{8} = 1.125$ m/s

The reason we subtract is because ${v}_{2} {t}_{2}$ is displacement south, which we've defined as negative.

If you chose south as the positive direction, then you'll get $- 1.125$ m/s as your final answer, since you'll be moving negative relative to South.