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(6 points} Solve Vit Vzr if V.(0,t) 0 = V,(1,) , "s.0) = 0 AIc Wl(z.0) = 2 C05 (27r) . Show the steps discusser] in lecture,...

Question

(6 points} Solve Vit Vzr if V.(0,t) 0 = V,(1,) , "s.0) = 0 AIc Wl(z.0) = 2 C05 (27r) . Show the steps discusser] in lecture,

(6 points} Solve Vit Vzr if V.(0,t) 0 = V,(1,) , "s.0) = 0 AIc Wl(z.0) = 2 C05 (27r) . Show the steps discusser] in lecture,



Answers

In Exerises $3-6,$ calculate the velocity and acceleration vectors and the speed at the time indicated.
$$
\mathbf{r}(t)=e^{t} \mathbf{j}-\cos (2 t) \mathbf{k}, \quad t=0
$$

In this trouble were given the acceleration. Victor. 00 on were given initial velocities at the time equals zero is equal to three on the initial position. The position of time was zero people here When my swing uh, the relationship between RV and they is that the is the derivative of far. Therefore, our is the integral of the everything on a you whom the root of the so the is going to be the integral of a. We start with this 50 you incur girl Hey 0 10 Integrating victim functions, rating components and in the derivative of 00 into the sea, plus a constant victims every day to name pardon, speak que in order to find B and Q We use the given condition for the of the era. On the one hand, when we plugging t equals here, here we get 00 speaking and on the other hand, were given that this is equal to 05 So we equate There are five with the zero Ah leave Teoh. This is a victor equation. First component must equal zero. Is there a mystical zero which is on five must equal zero sq which is secure. Therefore, veal, we come back here. P is equal to zero on cues equal to five. So v a t is going to be zero plus zero Vera and plenty 20 left foot. Which gives us the first half off. What we need to find the thick empire is going to be funding the position. The position faction is the integral off the coast. If actions are, he's going to be a girl off V A. T. I think which was the girl off? What we've got here. Zero 25. The T integrating component by component antidote to this zero 10 in the root of peace T squared plus into the route +55 plus Ah, constant Victor. We're whose components against the name unit, Uh, pendant to going to be careful here, So we will have that are easy. 05 square plus four C. Well, yeah, to find you here we use what we're given are zero are zero. On the one hand, it is equal to plugging in zero here. So 0505 times zero is zero. Yeah, um, using the given information that this is equal to one. Well, so one is equal to zero plus e you think and minus one is equal to zero profit, which is a so the function. Are you going back here? First component zero plus e. He's one first component is one second component is this Plus if if is minus one So we have five squared five See on this complete the things I needed to do. So this problem there is I hope it helps. No, but

Look in this problem. We are given the acceleration function to you given as one see component for, uh, the initial The lost velocity at time T Vera is given the victim to my on the initial position. Lucia Time t zero you, Leroy. The relationship between RV and they is that the the derivative of our so are is going to be integral. The a off the So these going to be an integral off a start with this, the f t the off to in control of a the team which is in Peru off one. The integrating component by component. This is the interpretive one, Steve. The interval of tes t squared over but a constant victory. Components were going tonight and pick you the five peaks here. We use the given initial condition here. So the off zero is on the one hand evaluating t zero Here. Here, give 00 plus speaking. And on the other hand, it's to minus one. Now we have a victor equality in which the first compartment two is equal to the sum of these p. The second component might swine is equal to the sum of the second component to this cute. Therefore V Off t if equal to to plus b we just to people he screwed up too. Bluff que, which is minus one. There we go. This completes the for part the problem. The second part of the problem is to find the, uh, position infections. So we employ this I see are off t the position faction is going to be the integrate over 50. So the interval of people t squared. Well, DT integrating component by component this is enter the discredit two plus two t on the second is one. Huh? Find Team Cube of three plus a cost victor, which were real. Name the components to simplify this a little bit. Okay, so we have a t squared of to duty is the first component. This is Cube of six months. Yeah, that fund es four years work were given here that the business reflection of T equals zero is there. Right. So are I. Zero is on the one hand, zero plus 0.0. The reminds. Your zero bluff. Yeah, and on the other hand, it is. You're all right. Zero. Okay. Applying the equality of Victor's the first component zero is equal to the sun. They're plus e e and ate. The second component is a second component will signal minute, which is, if therefore are tee. Our goal see is equal to this plus heat, which is zero. So the first component is T square of two plus two t and the second component is taking the six months the T u six months plus if which is a bluff on this complete work, we need to do in order to so this problem there, but but

Hello. In this problem, we are given the acceleration victor in three dimensions with component 00 thing Zeros wrote 10. And we are also given that the initial velocity or the the zero youth equal to the victory 50 And also we're given that the initial position is 050 intellectual 05 zero. My job is fine. What is the position? Faction, The velocity faction that since a is the derivative of the it follows that the is going to be the integral away So v A t is the integral off 00 thin they think integrating each components, integrating each component we have. And through those, they're 00 10. 30. Since the inspiration is, um, indifferent, we're going to her, um, adding to an anti derivatives a constant victor. We'll give the components names E if right that find the e f g components off the glass defection. We use what we are given that is, were given that the zero is on the one hand from 50 curative, on the other hand, plugging in zero, plugging in zero into this zero, Zahra. Sometimes there are three zeros. Plus, if victor quality means that we equate the first component through the first component. Sickened, sickened. And so so one is going to be equal to zero. Plus, there were five second component going to be second plus second, which is a Vera. Yeah, third component. Plus through. Okay. Which means that this victor here is 10 on the velocity. See you. This is the thing. Zero p is one. So the first complainant is one zero plus f f five, um, 10 t plus G is your This is what remains off. And we have the velocity. Victor, uh, for the rigid There. Now, from here, we find the position because he is the rebuttable position. Are is going to be the integral off the dating. So are we Is the integral off the one? Thanks. Do you think into the routers off one C five t and, uh, 10 times t have riches. Five t skirt. Both, uh, e one f one g one. Again. Another call it a two cost victor because the integration is different. Uh, to fine. He too. After Jason. Well, you've what we know about it are zero is where was given zero funds. Vera far euro on one hand, On the other hand, ground we plug in zeros here instead of tea, we have zero zero lira plus two it to meaning that zero equals The first component equals first plus first. The second component is five equals second component plus second component on 13.0 retreat third compound plus 13 ST meaning that are three Good bye is a C plus zero the first time. Five. The second component plus if two after a five second come plunges five p. And the third component is 50 squared plus GT GT zero on before pregnant. No really moment.

Hello. Oh, this is in this problem. We are given the acceleration. Big perfection. Ah, sci fi to fund. Fine. But, um uh, the initial velocity is getting your one the velocity off here, your world. The initial position Vera is given as far zero our job is to find with elections of the relationship between RV on a the core too far. The trolls are going to the people on a you, the derivative off velocity faction. Meaning that velocity will be obtained by integrating the You start with we integrate. Okay, Will be route the actual rate perfection. The interview. Oh, grow fine. All right. Farm on the truth. All signs mind In March 2 Love, uh, I have we have, but components will give your name to speak you the final pick here we use the initial. Yeah, the lofty. At times there is, on the one hand, zero my found zero. On the other hand, your one your foot. This is Victor. Equality. Victor. Quoted for the first component is zero vehicle to find your on one second people to here a reminder on the you're in a football. Uh, the coastline of zero. Well on fine. The why coordinate? All right, when is equal to Marthe? So we have Vera sold here. We have to do our five years equal. Three for a big queue. Here is three. Uh, your problem. You're, um the Do you find the murder thing? It's fine. Plus P p +05 the second component. 12 second preparing. Oh, problem right now. Are you want the girl off? Yeah. Are you Are you interviewing far too, Martin with mind. Fine. Ah, more with two times the colors of pro sign is fine. Okay. And see, while where you find components were used given initial off are we really is on the one hand. Mind miles to 50 left. 30 Look profound there. Well, find here. So we have, on the other hand, one of your reequip the first compartment with some components. So I have minus one. See, Marvel's second from zero. Uh, this is zero. Look during a to 15 and people lira. So here who euro meaning there are are vehicle the some of these minus 20. Um, the other component is adding zero to the off the problem. So it is Rippetoe. Truthfully, off course 30 is here three. Yeah. Uh, now, now. Okay, I hope, but


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