This is Chapter four. Problem number 114 were given a position makes for particle on the X Y plane position. Victor goes as to tea. I had plus to sign Pi ti over four j hat now in part they were asked the X and Y components at Time T equals zero Juan 234 seconds S o X component is you know is gonna be to t here. And the white component is gonna be to sign high tea over floor. So we'll only a we need to do is just playing in the the time here for you know, t zero people want people studio because three Teeples four seconds now, extent is gonna be when? Let's use this sort of notation The eggs, then at time equals zero seconds is gonna be cool to zero right x time equals one. Then two times one, he's gonna be two seconds. Two meters? Probably. These air, the position strike in the extraction T equals two seconds. Gonna be four meters. T equals three. Second is gonna be six mirrors, ext Eagles. Four second is gonna be eight meters now for why we're getting the same. It's just we have the sine function here. Why? He holds t zero second. Um, science zero. Brian's hand 00 Why? T equals one second. Regan is one here. Pi over four. Sign pi over four attempts to he's a spurt of tooth. And then why, tinkles? Two seconds is gonna give us. I have to, um, Times too. So power or two is one. So we're gonna get to from here. Why? It goes t three seconds. We're still getting square root of to break White was t four seconds we're getting for these are gonna cancel out Sign Pi zero. So we're getting back to zero now. We're asked to sketch the particles trajectory based on these positions in both x and y directions that became so you need to do is just draw If you want to put this on, you know, on a software that's fine. I'm just gonna sketch it because that's what we're asked. At the end, it's X valleys or 02 46 eight. So when where? Zero wise also zero. And then it goes to square root of two, then goes up to two and then comes back. So, um, when when we are at this is where time people zero. Right. So then the second point is actually here. And then the part made the turn point is here. And then we going back to spirit of two, right? And then we going back to zero action. So particles trajectory. Let me draw. Bad is the line that could extend these thoughts to each other. Right? All right. So again, this point is where t equals one teeth falls two seconds. He was three. TV goes four seconds right now in part B. This concludes part a party were asked Frank was velocity et velocity at T equals 123 seconds. So in order to get to the velocity, what we need to do is to take a derivative off the position vector that is given to us. If you do that, you're gonna find two. I had so distributable that signed term is gonna come out to me. Pi over two whole sign Pie t over four J hat. Right. So then then velocity When Teeples one is gonna be too. I had less 1.11 J hat velocity is gonna be 20 equals two seconds to I had because that's independent, right? Plus zero j hat because I'll sign 90 0 And then let's write 1/3 1 here. The t those three seconds. What we're getting is, too. I had now the opposite side. And why direction? And we're also said sketch that ensure that these velocities are tangential to the path. So that's easy, right? So t equals one second we're here, and you see that the both components are positive, So yes, and we might as well show it this one right handed me here across. Um, the cur here at this 0.2020 equals three. We have the negative of the same vector, Which means while the exes still positive. But why is negative? So then it's in this direction, right? So, yes, indeed, it's tangential. And look at this top point here, too. I purely in the extraction. Right. Can usual so that you can show. Um bye. Drawing vectors This way. Now in part. See? Well, next page artsy were asked what? The acceleration, the components of acceleration is in order to get through the acceleration. Um, really take one more derivative of the velocity vector is you know to get to the acceleration if we do that. Well, the I had terms disappears because going back here to the dirt off to zero derivative off this term comes out to be negative. Pi squared over eight sign I t over four j hat. So then X components, whatever time is asked which TV pulls one second people's a X. Teeples too of equals to a except T equals three seconds. They're all zero now, eh? Why, though, 20 was one comes out. Well, you need to do is just a plug in here, right? Signed by a pirate report and then times pi squared. Just put 3.14 pork, pork pie. What's gonna come out is negative 0.87 So sicken after what we're getting is and they get a 1.2. And the second after what we're getting is negative 0.87 of these air hand meters per second. Squared off course