What kind of graph do you get if you integrate a position-time graph?

Question

If you find the derivative of a position-time graph, you get a velocity time graph. If you integrate a velocity-time graph, you get a position-time graph. But what do you get if you integrate a position-time graph? I've heard many things including teleportation, time, and three dimensional motion. Thanks in advance.

Answer 1

The integral of a position-time graph is the total distance traveled during the time period which you integrated over, which is just another way of saying "weighed sum of all positions." And you can divide that by the total time to get your average velocity during this time period.

It is exactly as Nicknamr said, but I thought this may put it in better perspective.

Answer 2

If you integrate a position-time graph, you will get the weighted sum of position. Nobody does it because it isn't very interesting. You could, however, divide that by the total time and get the average position...