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

  • Thread starter piro
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  • #1
piro
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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)=[tex]\sqrt{Q(z)}[/tex] and everything else I can get by differentiating/integrating those two

The Attempt at a Solution


I have tried [tex]\int v(z) dz[/tex] 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...
 

Answers and Replies

  • #2
tiny-tim
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Homework Helper
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welcome to pf!

hi piro! welcome to pf! :smile:

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

i'm not sure what you're asking :confused:

but does this help? …

dv/dt = dv/dx dx/dt = dv/dx v = d(v2/2)/dx ?​
 
  • #3
piro
2
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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.
 

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