# An object travels North at  7 ms^-1 for 6 s and then travels South at  3  ms^-1 for  7  s. What are the object's average speed and velocity?

Jun 20, 2017

The average speed is $4.9$ $m {s}^{-} 1$

The average velocity is $1.6$ $m {s}^{-} 1$ North.

#### Explanation:

First step: find the distances traveled in each direction. We could also draw a diagram to the picture is clear in our heads.

We know $v = \frac{d}{t}$ and can rearrange to give $d = v t$.

For the movement North, $d = v t = 7 \times 6 = 42$ $m$.

For the movement South, $d = v t = 3 \times 7 = 21$ $m$.

Over all, then, the distance traveled (if we don't care about direction), is $42 + 21 = 63$ $m$.

The displacement (when we do care about direction) is $42 - 21 = 21$ $m$ $N$. Note that I included a direction.

The total time for both movements is $6 + 7 = 13$ $s$.

The average speed is $\text{distance"/"time} = \frac{63}{13} = 4.9$ $m {s}^{-} 1$

The average velocity is $\text{displacement"/"time} = \frac{21}{13} = 1.6$ $m {s}^{-} 1$ North.