find-the-acceleration-of-an-object-for-which-the-displacement-s-in-mathrmm-is-given-as-a-function-11

Question

Find the acceleration of an object for which the displacement $s$ (in $\mathrm{m}$ ) is given as a function of the time $t$ (in s) for the given value of $t.$
$$s=\frac{16}{0.5 t^{2}+1}, t=2 \mathrm{s}$$

Guilherme Barros · Accepted Answer

in this exercise were given the position of an object as a function of time here in the screen on the screen. And Maria asked to find What is the acceleration vector relate into this trajectory? So let&#x27;s first find what the velocity is. Let&#x27;s find the velocity vector. Let&#x27;s remind ourselves that the velocity vector is the derivative off the position with respect two time so V. It was the derivative of our with respect to time. Ah, so let&#x27;s do it Well, the first term is 3.2 t The derivative off tea with respect to T is one. So we only get to to the second term is 1.8 t square derivative of T Square is to t. So we&#x27;re gonna have to times 1.8 times t that is the 0.60. Okay, I and then the same thing for the the why component. It&#x27;s 1.7 minus 4.8 again, we&#x27;re just deriving only know Mia&#x27;s here. Well, you know, meals here j And then finally Ah, the exploration aid. The acceleration vector is the derivative off the velocity with respect to time. So it&#x27;s the V ditty. Uh for the first time term. The derivative off a constant is zero. So it&#x27;s simply gonna ah, disappear. The derivative of tea is one. So Ah, for the second term, we&#x27;re gonna have 3.6 i in the same thing for the second term. The first, the 1.1 point seven is gonna simply vanish. And the riveter of 4.8 times T is 4.8. Eso have for minus 418 Jay. So the final acceleration is through in six I, minus four point A J meters per second squared, and this is our final answer.

Ernest Castorena · Answer

they give us a position function with respect to time. Let&#x27;s see, the first component is for a T E to the negative to team and to e to the negative to team a negative 16 t squared. They want us to compute the velocity and acceleration functions. All right, I&#x27;m very These are just the first and second derivatives of the position function so we can compete. Those this is a vector valued function will compete that component ways. The first known require product rule will have four e to the negative duty. When we take the derivative of then add this time leaving t alone negative eight t e to the negative duty. Let&#x27;s see for the second component where you&#x27;re gonna have a negative foreign e to the negative duty and for the third component are going tohave negative 32. Okay, let&#x27;s take one more derivative to find our acceleration. Let&#x27;s here. We&#x27;re gonna have a negative eight e to the negative to t, but let me do product over this. This tea is going to disappear when we think it&#x27;s first derivative and we&#x27;ll have another negative eight e to the negative TV. Let&#x27;s just combine them both. Right now, we&#x27;ll have negative 16 e to the negative duty and let&#x27;s see that second product will relieve. This alone will have negative 80 times the derivative of either the negative fut Well, you multiply the whole thing by negative two. Then we&#x27;ll have a plus 16 t e to the negative duty. Okay, that&#x27;s the first component. The second component will just be eight e to the negative to t only take the derivative. Another components a constant negative there you to

Andrew Bassila · Answer

all right. In this problem, we&#x27;re going to find the instantaneous velocity from this position function, and the position function has given his FFT equals negative 16 t squared, plus five from using this definition over here, um, in the box for where? The limit of the different question. We&#x27;re going to do this for a equals one and equals two. But instead of doing this process with a equals one and then doing this process with a equals two, I&#x27;m gonna leave it as a and then back substitute so they don&#x27;t have to do this entire long process twice. So we&#x27;re gonna start with the limit of negative 16 times the quantity a plus age squared, plus five minus f of a. And we&#x27;re gonna leave it within a in there. We&#x27;re gonna put negative 16 a squared plus five. And again, I&#x27;m putting it in brackets which are just fancy parentheses because I need to distribute later. That&#x27;s all over H. So I&#x27;m going to distribute that negative sign and then expand a plus h squared, which, um, is a squared plus two a h plus h squared. But I know I&#x27;m in another room, so I&#x27;m gonna put it below here so that we don&#x27;t get crammed. So this is a limit as H approaches zero of Let&#x27;s leave the negative 16 out of it for right now, but it&#x27;s a squared plus two a h plus each squared plus five minus negative 16. So that&#x27;s plus 16 a squared minus five all over h. And then I&#x27;m now going to distribute this negative 16 in two, every term in the parentheses. And then I could maybe see what happened after that. So first up is writing my limit. Sometimes I forget this, but it&#x27;s important to remember you&#x27;re always taking a limit. This is going to be negative. 16. A squared minus 32 a. H minus 16 h squared plus five. And then I haven&#x27;t done anything over here, so that&#x27;s all going to stay the same. Now put this all over H. And I see that I can have two terms. Cancel the negative 16 a squared in the positive and then five and negative fiver five and minus five. Everything with an H survive. So I&#x27;m going to, um, factor out that each from both of these terms. So that&#x27;s an age times a quantity negative 32 a minus 16 h all over age. And I did that because I want these ages to cancel now and now I can dough do direct substitution by putting a zero in for every time I see H and I get negative. 32 A. This is my slope formula for the function that&#x27;s given in this case it the velocity formula, our velocity function because I was given a position function originally. So for part A, they want what happens at equals of one second. What&#x27;s the velocity? I just plugging a one and I get negative 32 feet per second or meters per second, depending on units for part B. I do the same thing. I just plug in a two now for a and I get negative 64 units per second.

Ernest Castorena · Answer

they give us a position function are of teeth is equal to Let&#x27;s see. The first component is 25. The second component. Let&#x27;s see, That&#x27;s a negative 16 T Square plus 15 team plus fire. And now they want us to find the velocity and acceleration functions well. The Velocity is just the first derivative of position and acceleration, which is the second derivative. Let&#x27;s go ahead and compete. Derivative, however, actor valued function. Let&#x27;s see, the director of the first component is just 25 of the second component. It&#x27;s negative. 32 t last 15. Nice spiral And then let&#x27;s see. Second derivative will get a constant zero. When you take that tribute and let&#x27;s see, we&#x27;ll get negative there, you to hear nothing.

Linh Vu · Answer

even the aspiration we confined adversity with the Internet culture, the Inter Columbia aspiration, the city and given when we get diversity, we can find the position function as they negotiated integral off the 50 de de it is question were given the aspiration 80 equal to the to the power t on strong. Given that the visual equal to one and and sterile equal to zero here the first time, we need to find the velocity function VT My family and culture the intercom that you, Egypt, DDT And we know that the constant you can bring outside So have the Jew integral in the each of the d d d. And we know integral um, the agility. It stays the same plus a constancy. And now we know that the we is equal to one so have a visible here, equal to the to evolve is zero plus c equal to one and again gets an equal to two plus C equal to one. Therefore, we have to see equal to the minus one and as a result, we got the verse DVD You must equal with you the ju each day minus one. This could be diversity function when again diversity function we can find policing function s they it will equal to the integral of diversity will be to each of the T minus one. Did they? And we know entirely river to him. This one will be staying the same but entirely river from the one equal to the day plus a constant say And now we know we were given the initial value on the answer equals zero. So we have the S zero here and we equal to the to each advisor or plus zero plus c equal to zero. That&#x27;s when we have the this one equal to two. Plus there are plus C equal to zero. It means that say we could you manage Thio However, on Uganda position function as they would equal to the to Egypt a d minus to the minus two

Problem

Find the acceleration of an object for which the …

Problem 37 Easy Difficulty

Find the acceleration of an object for which the displacement $s$ (in $\mathrm{m}$ ) is given as a function of the time $t$ (in s) for the given value of $t.$
$$s=\frac{16}{0.5 t^{2}+1}, t=2 \mathrm{s}$$

Answer

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Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus

Catherine R.

Kayleah T.

Kristen K.

Samuel H.

Precalculus Review - Intro

Functions on the Real Line - Overview

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Basic Technical Mathematics with Calculus

Catherine R.

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Precalculus Review - Intro

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Allyn J. Washington, Richard S. EvansBasic Technical Mathematics with Calculus

Catherine R.

Kayleah T.

Kristen K.

Samuel H.

Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus