# An object travels North at 1 ms^-1 for 3 s and then travels South at 7 ms^-1 for 5 s. What are the object's average speed and velocity?

May 23, 2016

The average speed is the total distance traveled divided by the total time: $\text{speed"="distance"/"time} = \frac{38}{8} = 4.75$ $m {s}^{-} 1$

The average velocity is the final displacement divided by the total time: $\text{velocity"="displacement"/"time} = \frac{32}{8} = 4.0$ $m {s}^{-} 1$

#### Explanation:

The average speed is the total distance traveled divided by the total time, while the average velocity is the final displacement divided by the total time.

The total time is $8$ $s$.

The distance traveled in the first $3$ $s$ is $d = v t = 1 \cdot 3 = 3$ $m$ North.

The distance traveled in the next $5$ $s$ is $d = v t = 7 \cdot 5 = 35$ $m$ South.

The total distance is $35 + 3 = 38$ $m$.

The total displacement is $35 - 3 = 32$ $m$ South.