Transforming velocity in terms of displacement to velocity in terms of time

[piro]

Homework Statement

I am modelling the motion of a space probe and have some problems with obtaining velocity in terms of time v(t). I am given Q(z)=v²(z). Q(z) is a solution to ODE which I have solved with z being the independent variable.

Homework Equations

Q(z)= something really nasty, I am keeping it in maple
v(z)=\sqrt{Q(z)} and everything else I can get by differentiating/integrating those two

The Attempt at a Solution

I have tried \int v(z) dz between 0 and t (the range of t and z is only positive) but the result is nonsensical and maple will not compute it

I have been messing around with maple for past couple of hours to no avail, so I might not be thinking straight and missing something idiotic...

 

[tiny-tim]

welcome to pf!

hi piro! welcome to pf!

(have a square-root: √ and an integral: ∫ )

i'm not sure what you're asking

but does this help? …

dv/dt = dv/dx dx/dt = dv/dx v = d(v²/2)/dx ?​

 

[piro]

i had more of a problem with Maple rather than with math


just solved the differential v(z(t))=dz/dt


however it didnt end up with a function that I could plot, despite being able to evaluate it at every point.