# Average velocity with respect to distance

Gold Member
In my Calculus class we had a problem to compare average velocity with respect to time vs. average velocity with respect to position.

Average velocity with respect to time is what is usually used in everyday language... "I drove to LA. I averaged 70 mph".

Then the Calc teacher asked what was the significance of expressing average velocity with respect to position. He said that there is a significance to it in Physics. Go ask your Physics friends...

Well... you people are my Physics friends. SGT
In my Calculus class we had a problem to compare average velocity with respect to time vs. average velocity with respect to position.

Average velocity with respect to time is what is usually used in everyday language... "I drove to LA. I averaged 70 mph".

Then the Calc teacher asked what was the significance of expressing average velocity with respect to position. He said that there is a significance to it in Physics. Go ask your Physics friends...

Well... you people are my Physics friends. Dimensionally it is the inverse of time.

Yeah.... heck. I think i got it. Average velocity wrt position mean the total DISPLACEMENT over total time. Taking your example of driving to LA, the person says, "I drove at 70mph..." So, if we assume he took one hour to travel the distance, he must have travelled 70 miles.

But, if you take say, average VELOCITY, its the magnitude of the vector joining the initial and final positions, over the time taken.

What you normally refer to as average velocity, is actually average speed. Velocity, is a vector, speed is a scalar. I think thats it.