how can one visualize an idea of "instant distance". seems a bit abstract that at some time "t" we can evaluate "instant distance" by *speed(t)*dt". imagine a speed versus time graph. now, there are two scenarios paradoxing in my head: if I assume that "dt" is a point on a time axis it seems that "no time has passed" (time freezed) and I can't visualize that something "moved" at speed(t) if there is no time interval. but if "dt" is some point (dt=0) surely we are gonna get instant speed(t) (like plugging "x" in some function f(x) and evaluating value of f(x) at that point "x") if I let some time "dt" to "pass" after "t" => t+dt than, surely, something "moved" by small amount and it seems reasonable to obtain distance traveled (but than it is not really "instant" distance at time t). looking at the function "speed(t)" if we have some time interval [t,t+dt] than there is some difference between speed(t) and speed(t+dt) and even if we calculate distance(t)=speed(t)*dt it doesn't look "instant" to me because of interval thing... help!