# An object travels North at 5 m/s for 6 s and then travels South at 8 m/s for 4 s. What are the object's average speed and velocity?

Jun 30, 2018

Refer to the explanation.

#### Explanation:

The total distance traveled was:

$5 \setminus \text{m/s"*6 \ "s"+8 \ "m/s"*4 \ "s}$

$= 30 \setminus \text{m"+32 \ "m}$

$= 62 \setminus \text{m}$

So, the average speed is:

$\overline{s} = \frac{d}{t}$

$= \left(62 \setminus \text{m")/(10 \ "s}\right)$

$= 6.2 \setminus \text{m/s}$

I'll take North to be the original direction for velocity. So, the total displacement is:

$5 \setminus \text{m/s"*6 \ "s"-8 \ "m/s"*4 \ "s}$

$= 30 \setminus \text{m"-32 \ "m}$

$= - 2 \setminus \text{m}$

So, the displacement is $2 \setminus \text{m}$ south.

The average velocity is therefore:

$\overline{v} = \frac{\vec{d}}{t}$

$= \left(- 2 \setminus \text{m")/(10 \ "s}\right)$

$= - 0.2 \setminus \text{m/s}$

This means that the average velocity is $0.2 \setminus \text{m/s}$ south.