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

May 9, 2017

${S}_{a} v$ of object is $= 2.4 \frac{m}{s}$

${V}_{a} v$ of object is $= \frac{4}{5} \frac{m}{s}$

#### Explanation:

The displacement of the object going $N$ for $1 s$ is:

$N - \left(\frac{4 m}{s}\right) \cdot 1 s = 4 m$

The displacement of the object going $S$ for $4 s$ is:

$S - \left(\frac{2 m}{s}\right) \cdot 4 s = 8 m$

We can take $S$ as the positive direction in this case where $N$ is opposite, so total displacement is:

$D = 8 m - 4 m = 4 m$

Time taken for the displacement is: $t = 5 s$

Average velocity is the displacement divided by the total time:

${V}_{a} v = \frac{4 m}{5 s} = \frac{4}{5} \frac{m}{s}$

The total distance traveled is #4m+8m=12m

Average speed is the distance traveled divided by the time.

${S}_{a} v = \frac{12 m}{5 s} = \frac{12}{5} \frac{m}{s} = 2.4 \frac{m}{s}$