ok, yes i see! but what is the resolution of Zeno's paradox? in one of Feynman's lectures (using the other example in which Achilles can run 10 times as fast as the tortoise but he can never catch the tortoise) he says "although there are an infinite number of steps (in the argument) to the...
oh, and rebound I'm not sure i understand why it's an exact value--isn't the idea to work with two points that are extremely close together so a curve looks like a line? but we're still working with slopes and spaces between two points, right? unless t actually = 0, which is not only undefined...
ok, i think i have a new but related question about this topic--when you take the derivative (dx/dt) and you let t-->0, doesn't the change in distance also end up going to 0? i know I'm misunderstanding something but it just seems like shrinking a value to almost nothing--how does it help?
ok, but isn't the way to calculate the rate of change of displacement with respect to time to use the derivative of the slope (dx/dt), conceptually minimizing the distance between the two points to almost zero?
thanks for the reply--but doesn't a limit never actually get to the value (for example, in a limit where x-->a, x never actually equals a?) you can have a graph where the limit is x approaching 5, but for the value of 5 the function f(x) can be anything, like 113 (i think)
can anyone verify my thought process here?
so, instantaneous velocity is like average velocity in that it is a slope between two points on a graph of position as a function of time
but the two points in a problem with instantaneous velocity are made to be extremely close, almost the same...