# An object travels North at 6 m/s for 4 s and then travels South at 3 m/s for 8 s. What are the object's average speed and velocity?

Jan 17, 2017

Its average speed is $4 \frac{m}{s}$ but its average velocity is zero, because at the end of its journey, it is back where it started.

#### Explanation:

To get the average speed, we need to find the total distance travelled.

$d = v \times t$

In the first $4 s$, the distance is $6 \times 4 = 24 m$. In the following $8 s$, the distance is $3 \times 8 = 24 m$ as well.

So, in total, the object has travelled 48 m in 12 seconds

$v = \frac{d}{t} = \frac{48 m}{12 s} = 4 \frac{m}{s}$

(Note that this is not what you would get if you added the two speeds and divided by 2, because the object spends different amounts of time at the different speeds!)

To find average velocity, we need to determine the displacement of the object. Since its first journey was 24 m north, and its second was 24 m south, it has arrived back where it started, for a net displacement of zero.

So, its average velocity is also zero.