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(10 points) A particle is moving with the given data. Find the position function s(t) of the particle_ "()er_7+6 s(u) =u...

Question

(10 points) A particle is moving with the given data. Find the position function s(t) of the particle_ "()er_7+6 s(u) =u

(10 points) A particle is moving with the given data. Find the position function s(t) of the particle_ "()er_7+6 s(u) =u



Answers

A particle is moving with the given data. Find the
position of the particle.
$$v(t)=1.5 \sqrt{t}, \quad s(4)=10$$

This is what we're given and to find the position. So for this, so we're going to take the anti derivative before we do. You're right. This has 1.5 T to the one half power here. It's a tribute to you. Okay, so finance or T. We're going to use Take the acid derivatives. We have 1.5 times T to the 3/2 Enterprise 3/2. So let's see 1.5. It's cool to 3/2, 32 times two thirds 10, 10, 3. or to see necessity. So now passive four equal to So that's 4 to the 3/2. Let's see must equal 10. So 4-3 to That's 2, 2 3rd c 10 pussy content. Therefore, C. Equals two. So our final S 30 it's going to be able to He's in a 3/2 was to

So trying to find the position of the particle. So we need to go back to the position function there. So hard to do this here you have to take the answer to read it twice. So we get you to first To give us t. cute over three. That is 40 squared over two. About six T. Plus C. Anti derivative with that again gets us. His city Equals 10 to the 4th over 12. This is two square so that's two T. To the third over three Plus 16 squared over two plus C. T. Plus D. Okay so that plugging into Sweet notes we have passive zero equals So then it's all zero here, Christie Cold cereal. So therefore team must equal zero Plug in. Once we have SF one Single to 1 12 last two thirds was three. Let's see 60 that we ignore that once the plus C. Of course 20. Okay so that this one right here is going to equal negative eight once so it's negative. It's 1 12 plus uh minus eight tops Plus three. So because track 3 to both sides here And I have c equals 17 And I'm gonna add 7/12 Because this overall is negative. 7/12 bringing to the other side I had. So then I'll have somebody calls to 11 over 12 for C. Our final answers Esselte Eagles. T to the 4th over 12 minus two thirds to to third Plus three T. Squared was to 11/12 teeth. That's the position

We're getting the following problem. You're told a of T is equal to t scoring minus 14. 06 And so there I was able to serve in excess of one as you go to 20. So first we need to find a bot, which we know it's anti absorbed over a of T, which will get us 1/3 T cube. When is to to squirt for 60 plus c Next, we need to find a sociologists and head over there. Beauty which will get us one well, t before minus 2/3 t cute Plus in three teams. Word plus ct Post E um, you know that s 00 is equal to zero. So we have zero people, too. 1/12 zeros. The fourth with 2/3 their O cubed plus three tons. Zero squared plus c. Time's up, Busty, you're left with these Equal to zero were some. Now that someone is you go to 20 soldiers. 20 is equal to 1/12 times. One to the fourth. This 2/3 of times one cube most three times one squared plus C times. One deal. We just now is equal to zero. So breaks off with this information. We know that we have 20 is equal to 29/12 courts. See, So you don't see is equal to 211 or 12. No one can plug it back. Interpersonal functions with US 15 people to warn 12 each before was to third T t cute plus three t squared plus 211 over 12 t. How is your answer?

So we see that we have a particle moving um with the given data and we want to find the position of the particle. So the velocity is be of tea or we'll call it F. Of X. Is equal to she squared minus three routine. Or three X. Will change this tax as well. This is our graph and we want to find the anti derivative anti derivative S. F. T. So we take the anti driver. This that's going to give us X cube over three and then the three fruit X. That's the same thing as three times X. To the one half. So the way that we would do that would be it would be uh minus three X. To the three halves over times two thirds. So it's gonna be minus two ax to the three halves plus C. Evaluating the position S. Of four equals eight. We get the eight third to see so have plus eight thirds. And then we see that jeep crime of X. He's going to end up giving us the same exact graph of F. Fedex, which means we evaluated this properly. So the anti derivative is G. Of X equals X cubed minus three minus two X 23 have plus 8/3 final answer.


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