Acceleration proportional to velocity

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Homework Help Overview

The problem involves a particle accelerated from rest with acceleration proportional to its velocity. The scenario includes determining the speed of the particle after it has traveled a certain distance, with specific values provided for distance and speed.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the relationship between acceleration and velocity, with some attempting to clarify the equations involved. Questions arise regarding the validity of certain mathematical manipulations, particularly concerning division by velocity.

Discussion Status

The discussion is ongoing, with participants providing insights into the mathematical relationships and questioning assumptions about the equations used. There is a focus on ensuring clarity in the definitions and manipulations of the variables involved.

Contextual Notes

Participants are exploring the implications of dividing by velocity and the potential loss of roots in the process. There is an acknowledgment of the original poster's adjustments to the problem's numbers, which may affect the clarity of the solution.

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Homework Statement


A particle is accelerated from rest with acc. proportional to velocity. After traveling 10 meters the speed is 35 m/s, find the speed after the particle traveled 20 meters. (Changed the numbers a bit from the original so the answer ppbly will not be clean.)

Homework Equations



a=v dv/dx possibly

The Attempt at a Solution


Sat on this one for a long, long time

Tanks in advance
 
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"Tanks"?

No, a is not "v dv/dx". Rather a= dv/dx which, here, is proportional to v:
a= dv/dx= kv for some number k.

From that dv/v= kdx. Now integrate both sides.
 
a = dv/dt, I think you mean?
 
Yea, watch out for those advancing tanks; hah, no I meant to say thanks.
Anyway, I do believe that a= v dv/dx ; dv/dt = (dv/dx)(dx/dt) = v (dv/dx). Does this seem reasonable:
a=kv=v dv/dx
k=dv/dx
k dx = dv
intg.
v=kx
? or is dividing by v not allowed => loss of roots or something?
 
I do believe you're right, a = v dv/dx. (In one dimension of course) And I don't see anything wrong with your work.

Can you think of a reason why dividing by v would not be allowed? (hint: what number(s) are you not allowed to divide by?)
 

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