Particle Distance/Velocity - Natural Logarithms

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Homework Help Overview

The discussion revolves around a problem involving the total distance traveled by a particle and its velocity, expressed through an equation involving natural logarithms. Participants are exploring the relationship between distance and velocity in the context of the problem.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • One participant expresses uncertainty about how to start the problem, particularly regarding the relationship between total distance and velocity. Another participant suggests determining when the particle stops and questions whether the velocity ever reaches zero, leading to a discussion about the implications of the equation provided.

Discussion Status

The discussion is ongoing, with participants providing hints and prompting the original poster to share their attempts. There is an acknowledgment of the complexity of the problem, and some guidance has been offered regarding the theoretical aspects of the particle's motion.

Contextual Notes

There is mention of the original poster's concern about inputting certain values in a submission box, indicating potential constraints in the problem setup or submission requirements.

Chase.
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Homework Statement



vDnRc.png


I'm going to post an image due to the complex syntax in the problem...

The Attempt at a Solution



I'm not going to lie... I really have no idea where to even begin with this problem. Because it says total distance traveled by the particle, I'm assuming that the total distance would be the distance equation multiplied by two; I'm not quite sure where velocity fits in however.

If I'm way off base, I'm still not looking for anyone to explicitly write out the answer for me. I just want to get headed in the right direction.
 
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First thing you have to determine is when the particle stops. Look at that equation: v(t) = v0 e^(-at). Does v(t) ever actually equal zero?

You need an infinite amount of time before the particle actually stops. In practical terms, the particle will be found to have slowed practically to a stop in a measurable amount of time. However, for this theoretical exercise, t has to be infinitely large before v becomes zero.

At this point, e^(-at) vanishes (becomes zero). Can you now find the value of s at this point?
 
Chase, the ball is back in your court. Show us what you have done, using the hints given by Courious3141 (this is, in fact, a very easy problem and Courious3141 gave very goo hint) or this thread will be deleted.
 
HallsofIvy said:
Chase, the ball is back in your court. Show us what you have done, using the hints given by Courious3141 (this is, in fact, a very easy problem and Courious3141 gave very goo hint) or this thread will be deleted.
I'm not sure why this response was so aggressive.

Anyway, thanks Curious! I figured it out. I had initially considered the v0/a solution but discounted it because I didn't think I could input v0 in the submission box.
 
Chase. said:
I'm not sure why this response was so aggressive.

Anyway, thanks Curious! I figured it out. I had initially considered the v0/a solution but discounted it because I didn't think I could input v0 in the submission box.

Glad you got it.:smile:
 

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