Inquiry on Dynamics (1 Viewer)

[beolun]

Hi, I was wondering if it was possible to convert velocity as a function of time to velocity as a function of position. I know it is possible if time is made a function of position through algebraic manipulation of the position function, although this becomes extremely messy and impractical for position functions which are polynomials of degree three or higher and other functions of such. New to Ext 2, thanks for the help.

 

[Sy123]

Hi, I was wondering if it was possible to convert velocity as a function of time to velocity as a function of position. I know it is possible if time is made a function of position through algebraic manipulation of the position function, although this becomes extremely messy and impractical for position functions which are polynomials of degree three or higher and other functions of such. New to Ext 2, thanks for the help.

So if we have then

 

[beolun]

My question was if I have v=f(t), how do I convert that to v=f(x) and what is the relationship between f(t) and f(x).

 

[Sy123]

My question was if I have v=f(t), how do I convert that to v=f(x) and what is the relationship between f(t) and f(x).

If the function is simple enough we can simply integrate a/v after a change in variable for x.

EDIT: Nvm this will result us in inding v in terms of x anyway.

Sometimes v cannot be a function of x valid for all positions x. i.e. in SHM, we have x=cos t, v= -sin t, we have 2 velocities for every position x.

Can you give an example where htis difficulty arises?

 

[beolun]

If the function is simple enough we can simply integrate a/v after a change in variable for x.

EDIT: Nvm this will result us in inding v in terms of x anyway.

Sometimes v cannot be a function of x valid for all positions x. i.e. in SHM, we have x=cos t, v= -sin t, we have 2 velocities for every position x.

Can you give an example where htis difficulty arises?

Lol, the reason I asked was because I have never seen it asked nor could I find any answer on google.