if you know the position vectors of a particle at twp points along its path and also know the time interval during which it moved from one point to the other...is it possible to determine the particle's instantaneous velocity and average velocity?

Question

anonymous · Answer

yes, for the average velocity between any two points but the position vector need to be a function to be instaneous

lgbasallote · Answer

so it's impossible to know the instantaneous velocity if the position vector is not a function?

anonymous · Answer

to the extent of my knowledge now

anonymous · Answer

unless you know all the point, which requires a really big table (infinitely big to be exact)

lgbasallote · Answer

position vector as function means something like x = 2t^2 + 3t - 1 where x = distance and t = time right?

anonymous · Answer

i'm a little rusty but, if that is parametric then that should be correct

lgbasallote · Answer

what does parametric mean?

anonymous · Answer

its basically a set of equations that are related by a common variable, but here it doesn't matter.

lgbasallote · Answer

oh okay..i thought it was a necessary term to learn

anonymous · Answer

i just remembered a position vector (at least in 2-d)
 is represented like this <x,y>. That equation you showed has average velocity:$$\Delta v/\Delta t$$ and instantaneous is basically the derivative of that equation