Displacement from velocity and time dependent force

[briteliner]

Homework Statement

The Force is F(x)=Av²/x. find x(t) if x(0)=0 and v_x(0)=0

Homework Equations

The Attempt at a Solution

My issue is that i set this up as mdv/dt=F but when i try to separate the variables i don't know what to do about the v since it depends on x. any suggestions?

 

[tiny-tim]

… My issue is that i set this up as mdv/dt=F but when i try to separate the variables i don't know what to do about the v since it depends on x. any suggestions?

Hi briteliner!

Standard trick …

dv/dt = dv/dx dx/dt (chain rule) = v dv/dx ​

 

[briteliner]

okay, so i do that.. and i get that (mv)dv/dx-kx(dv/dx)=0. can i cancel the dv/dx?

 

[tiny-tim]

… (mv)dv/dx-kx(dv/dx)=0 …

uhh? have you changed the question?