Hey, guys. In previous videos, we talked about the difference between distance and displacement to describe how far something moves. And in this video, we're going to talk about another pair of important, but related words called velocity and speed. Let's check it out.

So let's take a look at a familiar example. Let's say we were moving from A to B and then back to C again. We know that this is 10 meters to the right, and they're going to move 6 meters, and then we're going to be moving to the left here. There were two words to describe how far something moves. That was distance, which remember was given by the letter d, and was a scalar. Your distance is just the total of everything that you travel. So we know this totals 16 meters. The displacement, on the other hand, was a vector and it's the difference between where you started and where you ended, and it was the shortest path between those two points. And we know that your final position is 4, your initial position is 0. So your displacement, which is just 4 minus 0, was just 4 meters to the right.

So just like distance versus displacement, there are two words to describe how fast something is moving. And the basic idea here, guys, the main idea, is that speed is related to the distance that you travel whereas velocity is related to the displacement that's traveled.

Let's take a look at the equations. Speed is represented by the letter s and it's defined as the distance over time. Velocity is represented by the letter v and it's defined as the displacement over time. So the equations are as follows:

Speed = D Δt m/s

Velocity = Δx Δt m/s

That's going to be the units that we're working with over here.

Now, as speed is a scalar, it will always be either positive or 0 because it depends on the distance and distance can always just be positive or 0, it can never be negative. Whereas the displacement can be positive, negative, or 0, so your velocity can be positive, negative, or 0 because that's what your displacement can be. And so let's talk about negative velocity for a second. What does negative velocity mean? Remember, signs in physics just have to do with directions. So negative just means that you're moving in the opposite direction to whatever the positive direction is, and your problem is going to tell you what that direction is. So for example, let's say the right direction is positive, anything moving to the left is going to be negative. And sometimes, in rare occasions, you might see that the left direction is positive, your problem will tell you this, in which case anything that's moving to the right is going to be negative. So it just means whatever your problem tells you the positive direction is, anything moving to the opposite of that is going to be negative velocity.

Alright, guys. That's really all there is to it. So let's take a look at an example. We're going to jog 15 meters in 2 seconds, then 9 meters backwards in another 2 seconds. Let's calculate the speed and velocity. So, let's just draw a quick little diagram of what's going on here. So I'm going to move, I know this is going to be 15 meters in this direction. And then I'm going to move 9 meters backwards in another 2 seconds. So this is going to be 9 meters like this. So I know that the time here is going to be 2 seconds and the time here is also going to be another 2 seconds.

The speed is going to be calculated using the distance divided by ΔT. That's the equation that we have right up there. So, our total distance is 15 + 9 meters and our total time, is 2 + 2 seconds, making it 4 seconds total. So:

Speed = 24 4 ≈ 6 m/s

What about our velocity? Velocity is computed as Δx over ΔT for the whole trip. The shortest path from initial to final is actually from the start to where we ended after moving forwards then backwards. Thus, our displacement Δx = 15 - 9 meters, which equals 6 meters. Therefore:

Velocity = 6 4 ≈ 1.5 m/s

Since the displacement points to the right, the velocity vector also points to the right. That's it for this one, guys. This is the speed and velocity, and let me know if you guys have any questions.