# An object travels North at 9 m/s for 7 s and then travels South at 4 m/s for  6 s. What are the object's average speed and velocity?

Nov 18, 2017

average speed = 6.69 m/s
average velocity = 3 m/s

#### Explanation:

Given:

• Traveled north 9 m/s for 7 s
• Traveled south 4 m/s for 6 s

In order to answer this question, you must first know that speed and velocity are two different measures. Speed is a scalar quantity so it only takes into account the rate at which an object moves while velocity is a vector hence it involves both magnitude and direction.

Average Speed
So in order to get the average speed, calculate for the total distance the object traveled then divide the value by the time
since $\text{rate" = "distance"/"time}$ or in short $r = \frac{d}{t}$

$\text{distance going north} = 9 \frac{m}{s} \cdot 7 s = 63 m$
$\text{distance going south} = 4 \frac{m}{s} \cdot 6 s = 24 m$
$\text{total distance} = 87 m$
$\text{total time} = 7 s + 6 s = 13 s$

$\text{average speed" = 87/13 "m/s" = 6.69 "m/s}$

**Average Velocity#
Check the object's distance from the start point. Note that in this case since the object went north then went south, it technically went back nearer to its original position.

So using the computations above, we know that:

• Distance North = 63m
• Distance South = 24m

So distance from origin would be:
$63 m - 24 m = 39 m$

We know that $\text{total time} = 13 s$

So computing for the average velocity:
$v = \frac{d}{t}$
$v = \frac{39}{13} \text{m/s}$
$v = 3 \text{m/s}$

And now, here's a picture of Vector from Despicable Me so that you will always remember the difference between scalar and vector quantities!