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Average Speed and Velocity in 2D

Patrick Ford
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Hey, guys. So now that we've seen how displacement works in two dimensions in this video, I want to cover how speed and velocity work in two D what we're gonna uses a lot of the same equations that we use for one dimensional motion. But there's a couple of differences. So let's talk about those and to do a quick example. So 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 gonna be at some angle rather than just on flat line. But the idea is the same. So the difference between speed and velocity is that speed is a magnitude on Lee, and it's a distance over time. So Dior, Delta T and Distance is a scaler, so therefore, speeds the scaler. 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 Delta X over Delta T. But now we're working in two D. So we just use Delta. Are that's really all there is to it. So the magnitude is gonna be Delta are over Delta T. So now we're gonna have displacement vectors that point off its some angle like this. This is Delta are and this is the angle theta. So we also have to do now is specified the direction and the directions given by an angle fate of V And so here's the deal. If your velocity is given as the displacement overtime Delta, our delta T then what? Our direction your delta are points often that's gonna be the same exact direction as your velocity vector. So basically your velocity always points in the same direction as Delta are. And so whatever Theta V is, it's the same thing as data for Delta are they share the same angle. That's really all there is to it. Let's go ahead and do an example. So we're gonna walk 40 in the X axis and then 13 y, and the trip takes 10 seconds. So we know this is 40 and we know this is 30 and we know this is our delta t so we're gonna calculate the average speed in the first part and then the magnitude and direction of the velocity. So for the first part, we're gonna calculate the speed that's s and remember that is equal to, uh, distance over time. So it's d over Delta T. We know the Delta T is 10 seconds now. We just need to figure out the distance. So remember, I'm walking 40 in the X and 30 and the why these air both links that I'm traveling. And so that means that the distance is just the sum of all the links that I'm traveling. So that's 40 plus 30 and that's 70. So that means that my speed, this is gonna be 70/10 and that is 7 m per second on average. So that's my average speed. So let's move on down to the velocity. Want to figure out the magnitude of the velocity and I want to figure out the angle so the magnitude is gonna be Delta are over Delta T. That's the two dimensional displacement. So again, we know the Delta T is 10 seconds, but now we just need to go and figure out my two dimensional displacement vector. So remember, I'm walking 40 and 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 Delta are. And so how do we figure out the magnitude of this displacement? Well, this is just a triangle. We have the legs. This is 30 and 40. So this is a 345 triangle and that means Delta R is 50 m. So even though I literally walked 70 my displacement is only 50 m from start to finish. So that means that my the magnitude of my velocity is gonna be 50 m over seconds. So this is five meters per second now for the angle. Well, basically, the angle over here is gonna be this guy, this angle over here on dso remember that the angle for your velocity vector is gonna be the same thing as the angle for your displacement. So I've got the displacement vector, and I know that the velocity is gonna point off in this direction. So this is my V. And I know that they're going to share the same angle, Fada. So what I can do is I can just set up my tangent inverse equation, because that's the data. And I'm just gonna use the legs of the triangle. So I'm gonna use basically Delta y over Delta X. And so this is gonna be tangent inverse of over 40 and that's gonna be 37 degrees. So that is the magnitude and direction. Alright, guys, that's all there is to it. Let's go ahead and get some more practice.