Question

Is there a general formula for find Velocity-Position equation from Position-time equation?

Answer 1

If the position- time equation has an inverse, lets call it:
\[d^{-1}(x)\]
where d(t) is the position-time equation, then a velocity-position equation would be of the form:
\[d'(d^{-1}(x))\]
because you would plug the distance into the inverse to figure out how much time has elapsed, then you would get that time and plug it into the derivative of the position-time function.

Answer 2

this only works if the position time function has an inverse. if it doesnt, then you are out of luck.

Answer 3

Ok, thanks;
I am familiar position-time graph and velocity-time graph but not with velocity-position graph

Answer 4

yeah, you never really see velocity as a function of position, because only in a very cases is the position function invertible . If it was just like some car taking a trip, thats fine, but anything more complicated and it doesnt make sense.