 We have a squirrel that first goes to the left 10 meters in search of a nut, gets it, turns back and then travels another 25 meters to grab another nut. Let's say it takes the squirrel a total of five seconds to do all of this. The question we want to try and answer in this video is what is the average speed and the average velocity of this squirrel? So let's figure this out. Let's start with average speed. What is it? Well, we define average speed as the total distance traveled by the squirrel divided by the total time taken. So in this particular case, what is the total distance it travels? Well, it travels 10 meters and then 25 meters. Therefore, the total distance it travels is 35 meters and the total time it takes is 5 seconds. So average speed would be 35 meters divided by 5 seconds. That is 7 meters per second. There you go. That's the average speed. But now comes the question. What is average velocity? Well, for that again, we need to ask ourselves, what is the meaning of average velocity? Well, average velocity represents the squirrel's displacement divided by the total time. This time, we're not talking about the distance. We're talking about the displacement. But what does that mean? What is the meaning of the squirrel's displacement? To think about displacement, think about where the squirrel was initially at the beginning of that time, which is over here and then think about where the squirrel is finally. Don't think about the distance it travels. Just think about where the squirrel's final position is. Well, after going from here, at the end of that 5 seconds, the squirrel will be over here. So his final position would be here. Now, displacement represents how much the position has changed. That's what displacement is. Okay. So just from the diagram, can you answer the question? How much has the squirrel's position changed? Well, it was here to begin with. It has come here. So it has changed by an amount of 15 meters to the right. Can you see that? The squirrel has displaced 15 meters to the right. And now that we know the displacement, we can we can plug in over here and we can answer this question. So our average velocity becomes 15 meters displacement divided by the total time, the same time, 5 seconds. Right. So it took the displacement to 5 seconds. Okay. Now, remember the squirrel did not go from here to here. He did not travel 15 meters this way. He traveled like this. But when we are talking about average velocity, we don't care about his travel. We care about how much he has changed his location. That's all that matters. And how much has changed location is by 15 meters to the right. And therefore, if you divide this by 5 seconds, we will get the answer to be 3 meters per second. But remember, since displacement involves direction, see, if I just told you 15 meters, that won't tell you where the final location is. I have to tell 15 meters to the right. Only then you'll understand what the final location is, right? Therefore, I need to mention the direction. Displacement has direction in it. And so I have to mention it is to the right. So we would say that the squirrel was traveling, was displacing 3 meters per second to the right. And that is the squirrel's average velocity. Now, here's an important thing about the average value. See, if I say that we said the squirrel is traveling 7 meters per second over here, average speed, right? Does it mean the squirrel traveled every second, 7 meters? He went 7 meters in another 7 meters? No, we don't know about that. That's not mentioned. It's totally possible the squirrel traveled the first 10 meters in one second. Then maybe he traveled the rest 25 meters in four seconds. I don't know. Nothing is given. So then what does this number mean? This number means that if the squirrel had traveled at a uniform speed, if the squirrel never slowed down or speeded up, it was traveling at a constant speed. Then the number would be 7 meters per second. That's what this number is. That's what the meaning of average means. Average means assuming that things are constant. The rate is constant. The speed is constant. Okay. Same will be the case over here, even though it's really not. It's when you assume that the speed is constant or the, you know, the velocity is constant. When you do assume that and then you do the calculation, that's when we use the word average. Okay. Let's look at one more. This time we have a car that drives 50 meters to a shop. I don't know, maybe an ice cream shop or something. And then comes all the way back. And let's say the whole journey takes 20 seconds. The question we want to ask is what is calculated? What is average speed and average velocity? Again, can you pause this time and try to figure this out to yourself? All right, let's do this. So average speed is again, total distance divided by total time. What is the total distance? Well, he traveled 50 to the right, 50 to the left, so 100. So this time the total distance is 100 meters. What is the total time? 20 seconds. And therefore the average speed is five meters per second. Again, does this mean that the car traveled five meters every second? No, we don't know anything about it. Nothing is mentioned. Then what is the meaning of this five meters per second? This means that if the car traveled at a constant speed, if it did, we don't know that it does it, but if it did, then it would be traveling five meters per second. That's the meaning of the word average speed, assuming constant speed. Okay. Fine. Next, what is average velocity? Well, average velocity is displacement over time. What is the displacement here? Well, remember, displacement is change in its location, change in its position. Its initial position is here. Where is its final position? Hey, it's at the same location. So the car at the end of 20 seconds has not gotten displaced at all, right? So its initial and final locations are the same. Therefore its displacement is zero. So you get average velocity zero divided by 20 seconds. You get zero as the answer. Now this might sound confusing. Well, what does it mean? Like, does it mean the car did not travel? No, no, car did travel. You see, it did have average speed. It did travel. But remember, velocity represents how much the car got displaced, how much the car changed its location. And at the end of 20 seconds, it has not changed its location at all. It is back to its same original location. And that's why we say the average velocity is zero because it is this one is zero.