![]() They're not the same thing to don't get confused there. The only thing we have is the magnitude and direction of the final velocity vector. But if we take a look here, we actually don't have the acceleration, vector, the magnitude or the direction. We could either use the change in the velocity and time, or we can use the magnitude and the direction of the of the acceleration vector. So how do we calculate the components off this acceleration Vector over here. The magnitude and the direction both change. We know the final velocity here, 67 we know this angle here is 26.5 degrees. Now it's actually moving at some angle above, so it's basically moving at some angle like this. This is my initial, and then my final is where the velocity is not moving just along the X axis. So we have this toy car that is initially moving, so this is my initial velocity At 20 m per second. But before we get to that, I just want to draw a quick sketch of what's going on here. So for part, A were asked for a X and A Y. So in this first part of the problem, we're gonna calculate the X and Y components off the cars acceleration. ![]() All right, so we have a toy car that's moving initially at 20 m per second and then later on it's moving at at some angle. So let's just go ahead and jump right into an example. They're different, they work the same exact way. So the equations are very similar against really just the letters. So if we have a and theta than a X and Y are just a co sign data and a sign data. There now we could also calculate this A these a X and A Y components by using the magnitude in the direction of the acceleration vector. Remember that if the two dimensional acceleration is change in velocity over change in time, then the acceleration in the X direction is just the change in velocity in the X direction over time and the change in velocity and the Y is gonna be the change in velocity in the Y direction over change in time. If you have Delta X and Delta T or if you had the magnitude and direction off that two dimensional vectors, those two different equations well, it's the same kind of idea for the acceleration vector. Remember velocities always displacement over time, so velocity and the X direction was either calculated. Okay, so let's look at the components now of the acceleration vector Now for the velocity components. It's the same thing for the angle, for the acceleration is just the tangent adverse of a Y over X was nothing really new there. Right? Three angles always tangent adverse off V Y over Vieques. So the angle of this vector here is just related to the components by the tangent universe equation. So if you're giving Delta V and Delta T, you can calculate the magnitude of a or if you're giving the components a X and a Y, then you can calculate the high partners through the triangle by using the Pythagorean Theorem X squared plus a Y square All right, let's move on. You could either always relate this to the change in velocity of a change in time. The same exact thing works for acceleration. And so the high pot news of the magnitude, it's just the Pythagorean theorem v x squared plus view I square. It's really just only the notation that's different. Well, from now on, we're actually gonna start drawing all the components starting from the same point like this. Now, up until now, we've always visualized these sort of magnitudes directions and components as triangles because they help us visualize all the triangle equation that we're gonna use. In time, we calculate V or we could use the components of the vector so we would take this two dimensional vector and break it up into its components VX and vy y. So for for the velocity vector in two dimensions, we had two different equations to calculate the magnitude. It's just that now that we have things that angles, all right. It's gonna work the exact same way in two dimensions. So the equation that we use was a equals Delta V over Delta T. And this actually works for one dimensional motion or two dimensional motion at an angle. It changes either the magnitude or the direction of the velocity or sometimes even both. Alright, guys, remember that acceleration always causes a change in objects velocity. So let's just talk about the differences and then do a quick example. It's really only just the letter that's different. These equations are gonna look almost identical. We're gonna end up with a very similar set of two equations to jump back and forth between the acceleration and its components. What we're gonna see is that it works very similar to how velocity in two dimensions works. ![]() So not in the X or why, but at an angle like this. Hey guys, you may be asked to calculate the acceleration of an object that's moving in two dimensions.
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