What is the velocity and time needed to solve this kinematics problem?

AI Thread Summary
The discussion revolves around solving a kinematics problem involving a particle with acceleration defined as a = -k√v. The user seeks assistance in determining the particle's velocity at x = 24 m and the time required for it to come to rest, given initial conditions of x = 0, v = 81 m/s at t = 0, and v = 36 m/s at x = 18 m. The user attempted to use the equations a = v(dv/dx) and a = dv/dt for integration but encountered difficulties. Other participants are encouraged to share their calculations and insights to help resolve the issue. The user expresses willingness to return for further assistance if needed.
lidakeo
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Hi guys. I'm new here. If i did any mistake please forgive me.



First of all I have a simple problem need all of you to help me.



Here is the problem


The acceleration of a particle is defined by the relation a = -k√v, where k is constant.
Knowing that
x = 0 and v = 81 m/s at t = 0
and v = 36 m/s x = 18 m

determine
(a) the velocity of the particle when x = 24 m
(b) the time required for the particle to come to rest.
 
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using ##a=v\frac{dv}{dx}## or ##a=\frac{dv}{dt}## and some integration, can you find a relation between v and x?
 
MrWarlock616 said:
using ##a=v\frac{dv}{dx}## or ##a=\frac{dv}{dt}## and some integration, can you find a relation between v and x?


I did but it not work for me. Maybe I missed some part. I'll try again. Thank for reply.
 
You can post your calculations if you are stuck. :smile:
 
MrWarlock616 said:
You can post your calculations if you are stuck. :smile:

I'll reply back. If I got stuck again. :smile:
 
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