To talk about the differences between speed and velocity, let's talk about how they are defined.
Speed can be defined as the distance traveled divided by the total time taken. So, speed = distance/time.
While velocity can be defined as the displacement divided by the total time taken. So, velocity = displacement/time.
Now, let's imagine a person who ran around a circular park and returned to the same spot that he started from. The person would have covered a certain amount of distance around the circular park in a certain amount of time. If the person ran really fast, he would have used up less time to run around the park, and thus he would have a high speed. But if he ran really slowly, he would have used up more time to run around the park, and thus he would have a low speed. This part seems rather intuitive for now.
But, let's move on to velocity. Because the person ran back to his starting position, he would have zero displacement. Displacement is the difference in distance between the starting and final position. So, since displacement is zero in this case, we can say that the running man has an average velocity of zero!
So speed depends on distance traveled, while velocity depends on the displacement.
I'd also like to point out that speed is just a number (e.g. 10m/s or 24km/hr). However, when we talk about velocity, we usually have to describe the direction as well (e.g. 10m/s northwards or 24km/hr eastwards). It's because the velocity changes when the direction changes that the velocity can average to zero even though it isn't zero at any particular time.
In our daily lives, because the magnitude of the velocity at a particular moment of time is the same as the speed at that particular moment of time, we do not really make a huge fuss about the difference between velocity and speed.
(published on 04/20/12)