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

In summary, the conversation discusses the difficulties in obtaining velocity in terms of time for a space probe motion model. The equations involved are Q(z)=v2(z) and v(z)=√Q(z), and attempts have been made to solve for v(t) using Maple. Despite solving the differential v(z(t))=dz/dt, a plotable function has not been obtained.
  • #1
piro
2
0

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...
 
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  • #2
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
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.
 

1. What is the equation for transforming velocity in terms of displacement to velocity in terms of time?

The equation for transforming velocity in terms of displacement to velocity in terms of time is:

Velocity (in terms of time) = Displacement / Time

2. Why do we need to transform velocity in terms of displacement to velocity in terms of time?

We need to transform velocity in terms of displacement to velocity in terms of time because it allows us to calculate the average velocity of an object over a specific time period. This can be useful in analyzing the motion of objects and understanding their acceleration.

3. How is velocity in terms of displacement related to velocity in terms of time?

Velocity in terms of displacement and velocity in terms of time are related by the equation: Velocity (in terms of time) = Displacement / Time. This means that the two values are directly proportional to each other.

4. Can you give an example of transforming velocity in terms of displacement to velocity in terms of time?

Sure, for example, let's say a car travels 100 meters in 5 seconds. To calculate the velocity in terms of time, we would use the equation: Velocity (in terms of time) = Displacement / Time. So, the velocity would be 100 meters / 5 seconds = 20 meters per second.

5. How does transforming velocity in terms of displacement to velocity in terms of time help us understand an object's motion?

Transforming velocity in terms of displacement to velocity in terms of time helps us understand an object's motion by giving us a measure of the object's average speed over a specific time period. This can be used to analyze the object's acceleration, which can provide insights into its overall motion and behavior.

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