What happens to motion when the derivative of radial vector is negative?

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stunner5000pt
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Please help! Motion problem

Suppose one found the equation of a radial vector with respect to time.
Then if one were to differentiate it with respct to time and find the value of r'(t=0)
suppose that was value was positive then the velocity is positive
if negaitve then the velocity is negative
but what about the subsequent motion? keep in mind that the r(phi) where phi si the polar angle is given by an exp function.
I understand that if r'(0) > 0 then it will proceed with positive displacement
but hwat about the negative??

this is a follow on from this question https://www.physicsforums.com/showthread.php?t=106913
 
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I am confused by your question. Are you working in one dimension here? If so then the polar angle is fixed. And if not then it makes no sense to talk about the sign of the velocity. What is the sign of the [itex]\mathbb{R}^2[/itex] vector [itex]<-1,3>[/itex]? You can't define it because [itex]\mathbb{R}^2[/itex] vectors aren't ordered like the reals are.
 
By the way stunner, these threads that you've been posting in Introductory Physics would acutally qualify as Advanced Physics, so I'm moving them. I think you will have better luck getting responses here.