# Distinguish between instantaneous speed and instantaneous velocity

I encountered a line in my text book of physics that:

Average speed over a finite interval of time is greater or equal to the magnitude of the average velocity. But instantaneous speed at an instant is equal to the magnitude of the instantaneous velocity at that instant.

Now the question is how

instantaneous speed = | instantaneous velocity |?

• magnitude of the velocity vector gives speed... – Eliza Jan 19 '14 at 14:30
• @Eliza what you are saying is that true in general. Just take an example where body after motion return to its original position in that case magnitude of velocity is zero but not the speed.Think over it. – Singh Jan 19 '14 at 15:05

## 1 Answer

The definition of speed is the magnitude of velocity.

To understand how the "average speed over a finite interval of time is greater or equal to the magnitude of the average velocity" consider the following example:

For 5 seconds you travel at +10m/s in a straight line. Then, you turn around and travel -10m/s for another 5 seconds in a straight line arriving back at where you started. During the entire trip, your speed is 10m/s and thus your average speed is 10m/s. However, during half the trip your velocity was positive 10m/s and the other half it was negative 10m/s, so your average velocity is 0m/s. The magnitude of 0m/s is 0m/s. Thus your average speed is greater than the magnitude of your average velocity.