An object travels North at 3 m/s for 8 s and then travels South at 4 m/s for  2 s. What are the object's average speed and velocity?

Aug 20, 2016

We must recall the definitions of average speed and average velocity.

Average speed: the change in distance divided by the total time

Average velocity: the DISPLACEMENT divided by the total time

remember that DISPLACEMENT is the distance from the initial point and the final point. So if I ran one lap around the track field, my displacement would actually be .... 0 meters.

So, we want to find the total distance that we traveled, both North and South.

traveling 3 m/s for 8 s would mean that we traveled for 24 meters total, North.

traveling 4 m/s for 2 s would mean that we traveled for 8 meters total, South.

Therefore, our total distance is 32 meters. The time it took was 10 seconds (8s north and 2s south), so the average speed is
$\frac{32}{10} = 3.2 \frac{m}{s}$

Part 2
Our total DISPLACEMENT is going to be 24 north + 8 south, or basically if we take north as the positive direction,  24+(-8) or 16 meters positive, or 16 meters north.

Our total time is still 10 seconds, so our average velocity is

$\frac{16}{10} = 1.6$ m/s North