# An object travels North at  4 m/s for 1 s and then travels South at  5 m/s for  3 s. What are the object's average speed and velocity?

May 14, 2017

Average Speed: $4.75$ m/s
Average Velocity: $- 2.75$ m/s

#### Explanation:

To calculate the object's average speed (direction doesn't matter), we use the formula:
${s}_{a v g} = \left(\text{total distance")/("change in time}\right)$

We know that the object traveled for 4 m/s for 1 s then traveled 5 m/s for 3 s, therefore:
$4 \left(1\right) + 5 \left(3\right) = 4 + 15 = 19$ is the total distance traveled in meters
$1 + 3 = 4$ is the change in time

Therefore,
${s}_{a v g} = \frac{19}{4} = 4.75$ m/s

To calculate the object's average velocity (direction matters), we use the formula:
${v}_{a v g} = \left(\text{displacement")/("change in time}\right)$

Let North be positive and South be negative. We know that the object traveled +4 m/s for 1 s then traveled -5 m/s for 3 seconds, therefore:
$4 \left(1\right) - 5 \left(3\right) = 4 - 15 = - 11$ is the total displacement in meters
$1 + 3 = 4$ is the change in time

Therefore,
${v}_{a v g} = - \frac{11}{4} = - 2.75$ m/s