Help needed with integration problem

[Guest]

Hi Guys

Im reading a research paper and going through the equations therein and have come across a part I cant solve.

I dont want to just use the papers equations without understanding how they were derived so any help with this bottleneck would be really appreciated

Heres what the paper gives:


Vr = wV/2Nr


where Vr is radial velocity = -dr/dt

We need to solve for r.


the paper gives the initial condition, r=ro at t=0 (where ro is a constant)



It then gives a solution for r as:- r= (ro^2- (wVt/N)^0.5


I just cant see how they get that.....

can anyone shed any light on this?


Much appreciated

[Guest]

heres what i assumed,


Vr = -dr/dt

so -dt/dr = wV/2Nr

at r=ro t=o

so rewriting -dt/dr = wV/2Nro

Intergrating with respect to t


-r = wVt/2Nro

which looks nothing like what the paper shows....

[Guest]

sorry that should read -dr/dt = wV/2Nro