An object travels North at 6 m/s for 2 s and then travels South at 6 m/s for 7 s. What are the object's average speed and velocity?

May 25, 2018

Refer to the explanation.

Explanation:

Average speed is defined through the equation:

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

where:

• $\overline{s}$ is the average speed

• $d$ is the total distance covered

• $t$ is the time taken

So, we get:

$\overline{s} = \left(6 \setminus \text{m/s"*2 \ "s"+6 \ "m/s"+7 \ "s")/(9 \ "s}\right)$

$= \left(54 \setminus \text{m")/(9 \ "s}\right)$

$= 6 \setminus \text{m/s}$

Velocity is given by the equation:

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

where:

• $\overline{v}$ is the average velocity

• $\vec{d}$ is the distance covered in a specific direction

• $t$ is the time taken

Here, I'll let the standard direction to be north. So, the south direction will be represented as negative.

So, we get:

$\overline{v} = \left(6 \setminus \text{m/s"*2 \ "m/s"-6 \ "m/s"*7 \ "s")/(9 \ "s}\right)$

$= \left(- 30 \setminus \text{m")/(9 \ "s}\right)$

$= - 3. \overline{3} \setminus \text{m/s}$

Therefore, the average velocity is $3.33 \setminus \text{m/s}$ south.