Hey, guys. So now that we've seen how displacement works in 2 dimensions, in this video, I want to cover how speed and velocity work in 2D. What we're going to use is a lot of the same equations that we use for 1-dimensional motion. But there are a couple of differences, so let's talk about those and then do a quick example. Just remember that speed and velocity just measure how fast something is moving between two points. The only thing that's new here is that these two points are going to be at some angle rather than just on a flat line. But the idea is the same. So the difference between speed and velocity is that speed is a magnitude only and it's a distance over time. So d/Δt and distance is a scalar, so therefore speed is a scalar. On the other hand, velocity is a magnitude and a direction. It's not distance over time. It's displacement over time. Displacement is a vector and so therefore, velocity is also a vector. So the only thing that's new here, guys, is that in one dimension, we use the one-dimensional displacement Δx/Δt. But now we're working in 2D. So we just use Δr. That's really all there is to it. So the magnitude is going to be Δr/Δt. So now we're going to have displacement vectors that point off at some angle like this. This is Δr and this is the angle theta. So what we also have to do now is specify the direction and the direction is given by an angle θ_v. And so here's the deal: If your velocity is given as the displacement over time, Δr/Δt, then whatever direction your Δr points off in, that's going to be the same exact direction as your velocity vector. So basically, your velocity always points in the same direction as Δr. And so whatever θ_v is, it's the same thing as theta for Δr. They share the same angle. That's really all there is to it. Let's go ahead and do an example.

So we're going to walk 40 in the x-axis and then 30 in the y-axis and the trip takes 10 seconds. So we know this is 40 and this is 30 and we know this is our delta T. So we're going to calculate the average speed in the first part and then the magnitude and direction of the velocity. For the first part, going to calculate the speed. That's s. And remember that is equal to, distance over time. So it's d/Δt. We know the Δt is 10 seconds. Now we just need to figure out the distance. So remember, I'm walking 40 in the x and 30 in the y. These are both the lengths that I'm traveling. And so that means that the distance is just the sum of all the lengths that I'm traveling. So that's 40 plus 30 and that's 70. So that means that my speed is going to be 70 over 10, and that is 7 meters per second on average. So that's my average speed. So let's move on now to the velocity. I want to figure out the magnitude of the velocity and I want to figure out the angle. So the magnitude is going to be Δr/Δt. That's the 2-dimensional displacement. So again, we know that Δt is 10 seconds, but now we just need to go and figure out my 2-dimensional displacement vector. So remember, I'm walking 40 30, so I'm walking literally 70 in terms of distance. But my displacement is the shortest path from start to finish. So that's this angle or this vector over here. This is Δr. And so how do we figure out the magnitude of this displacement? Well, this is just a triangle and we have the legs. This is 30 and 40. So this is a 3, 4, 5 triangle and that means Δr is 50 meters. Even though I literally want 70, my displacement is only 50 meters from start to finish. So that means that the magnitude of my velocity is going to be 50 meters over 10 seconds. So this is 5 meters per second. Now for the angle. Well, basically, the angle over here is going to be this guy, this angle over here. And so remember that the angle for your velocity vector is going to be the same thing as the angle for your displacement. So I've got the displacement vector and I know that the velocity is going to point off in this direction. So this is my V, and I know that they're going to share the same angle theta. So what I can do is I can just set up my tangent inverse equation because that's the theta, and I'm just going to use the legs of the triangle. So I'm going to use basically delta y over delta x. And so this is going to be tangent inverse of 30 over 40, and that's going to be 37 degrees. So that is the magnitude and the direction. Alright, guys. That's all there is to it. Let's go ahead and get some more practice.