 So let's look at the definitions of displacement, distance traveled, instantaneous velocity, instantaneous speed and average velocity and average speed on an example. So we have here a graph of a movement where somebody moved from 1 meter to 5 meters within 4 seconds, then stayed there for 2 seconds and traveled back to 1 meters per second arriving here at 8 seconds. So what is the total displacement? The total displacement is the final position minus the initial position. So we arrive at 1, we get back to 1, so the total displacement in this case was 0 meters. Note that displacement could have been a vector from 0 to 4 seconds, the total displacement was plus 4 meters. So here we had plus 4 meters, while from 6 to 8 we had a displacement of minus 4 meters. So a vector meaning it had a sign. Now what's the total distance traveled? Well of course the distance traveled is the 4 meters we traveled up plus the 4 meters traveling down gives us 8 meters. Then the instantaneous velocity, this is what we have plotted on the velocity time graph using our rules of slope or derivation to find the velocity at any moment in time, so instantaneous velocity. Now what would be the instantaneous speed? Instantaneous velocity was a vector as well because we had plus or negative signs giving us directions. Instantaneous speed would have been the same thing, just everything positive. So this one here we would flip to the positive, so no big thing. What gets interesting is for average velocity and average speed. For average velocity the rule is we take the displacement and divide it by time. So according to this formula in this case our average velocity was 0 meters per second. Now can this be? We can calculate it also as the weighted average. So we had for 1, 2, 3, for 4 seconds we were traveling at plus 1 meters per second. Then for 2 seconds we were traveling at 0 meters per second. And then for another 2 seconds from 6 to 8 we're traveling at minus 2 meters per second. Now if you do the weighted average 4 times plus 1 is plus 4, plus 2 times 0, plus 2 times minus 2 gives me 0 again, divided by the total time 4 plus 2 plus 8 gives me exactly the 0. So there are actually two ways of finding the average velocity. For the average speed we take the displacement over time. So we had 8 meters over what was my time 8 seconds total over 8 seconds, which gives me an average speed of 1 meters per second. Again this is not a vector so here we're just giving the 1 meters per second. Now for speed we could look at the same thing if we do the weighted average if we get the same thing. For the first 4 seconds we had 1 meters per second. Again for speed I'm looking at the time. Then for 2 seconds we had 0. And then for the last 2 seconds we were traveling at 2 meters per second of speed. So we get 4 seconds times 1 meters per second plus 0 seconds times 0 meters per second plus 2 seconds times 2 meters per second over a total of 8 seconds. So I get 4 plus 4 is 8 is 8 meters over 8 seconds is 1 meter per second. So I get the same thing from the weighted average or I can use this shortcut formula. Distance traveled over time and for velocity can use the displacement over time.