Acceleration and distance using derivatives.

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Homework Help Overview

The discussion revolves around the concepts of acceleration, velocity, and distance in the context of derivatives and integrals. Participants are exploring the relationships between these concepts and how to apply them to a specific problem.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss the differentiation and integration processes related to velocity and acceleration. Questions arise about the correctness of the differentiation and integration steps taken, as well as the application of the chain rule and substitution methods.

Discussion Status

Some participants have provided guidance on the differentiation and integration processes, while others are still questioning their understanding of the methods involved. There is a mix of attempts to clarify concepts and verify the correctness of the approaches taken.

Contextual Notes

There are indications of uncertainty regarding the application of integration techniques, particularly with respect to the substitution method. Participants are also navigating the challenge of limited knowledge about certain functions, such as e^x.

Bman900
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Now I understand the basic concept that if one derivative's velocity you get acceleration and if you integrate velocity you will get the distance. But what about in this case?

Homework Statement


problem1.jpg

Homework Equations


The Attempt at a Solution


attemptedsolution-1.jpg
 
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You didn't differentiate properly. You need the chain rule(s).

So, I'm thinking you probably didn't integrate correctly, either.

But, we don't know, as you didn't post your results.
 
Well I didn't get to that yet because I was not sure that is the correct way of finding the answers. So am I at least derivating the right parts of the equation?
 
For what the problem is asking, yes - that's the correct approach.
 
Ok so I derivated but I could not integrate because I have only know e^x. Am looking into to solving that but please tell me if the answers so far are correct?

attemptedsolution-2.jpg
 
The a_x is correct, but not a_z. What is the derivative of cos?

And for the integration, set -2t to u, so that you integrate e^u. Don't forget that you are now integrating with respect to u!
 
Oh its -sin so the negative signs cancel out! Thanks. Am am about solve the integral here soon as I have to learn a bit more about the substitution method.
 
Am I correct?

integrate.jpg
 
Looks good to me!
 

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