Acceleration and Velocity Relationships

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Homework Help Overview

The problem involves the relationship between acceleration and velocity for a particle, defined by the equation a = -10v. The original poster presents a scenario where the particle starts with an initial velocity of 30 m/s and poses several questions regarding the distance traveled before coming to rest, the time required to stop, and the time to reduce velocity to 1 percent of its initial value.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants discuss the application of the equation a = dv/dx and express uncertainty about solving for acceleration as a function of velocity. There are attempts to derive expressions for velocity over time, with some participants questioning the implications of the particle never coming to a complete stop.

Discussion Status

The discussion is ongoing, with participants exploring different interpretations of the problem. Some guidance has been offered regarding the integration of velocity to find distance, and there is acknowledgment of the theoretical aspects of the particle's motion.

Contextual Notes

Participants note the potential for infinite time and distance in the context of the problem, raising questions about the assumptions underlying the scenario. There is also mention of language barriers affecting communication.

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Homework Statement



the acceleration of aparticle is defined by the relation a=-10v , where a is expressed in m/s2 and v in m/s knowing that at t=0 the velocity is 30 m/s
determine
(a) the distance the particle will travel before coming to rest
(b) the time required for the particle to come to rest
(c) the time required for the velocity of the particle to be reduced to 1 percent of its initial value

Homework Equations



a=dv/dx or vdv/dx

The Attempt at a Solution



hmm well I am not sure how to solve acceleration in function of velocity
 
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hello,

a = dv/dx is the right formula. where are you getting stuck?
 
everytime i solve it i get stuck at (v=30e^-10t) so can't make v equal 0 since it will be undefind :S
 
yes, that is the correct solution. i agree that the first two questions do not make sense since the particle, theoretically, does not stop; well, i guess they make sense if infinity is allowed as an answer. the third you should be able to answer with your solution.
 
yes i did answer the 3rd one and its easy...the 1st and 2nd r suxx :P
ty for help :)
 
cheers
 
you know, now that i think about it, the first question might have an answer, if we integrate v from 0 to infinity, i am almost certain that integral converges. you might want to check that.
 
hmm I am not sure what do u mean? can u write the equation please? sorry but english aint my native language
 
i am thinking that the total distance traveled will be given by the expression:

[tex]d = \int_{0}^{\infty}{v(t)}dt[/tex]

and i believe this will converge to a finite distance. though it will still take an infinite time to get there!
 
  • #10
lol ill try to work on that
 
  • #11
good luck. :smile:
 

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