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

[lidakeo]

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.

 

[MrWarlock616]

using $a=v\frac{dv}{dx}$ or $a=\frac{dv}{dt}$ and some integration, can you find a relation between v and x?

 

[lidakeo]

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.

 

[MrWarlock616]

You can post your calculations if you are stuck.

 

[lidakeo]

You can post your calculations if you are stuck.

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