Quote:
Originally Posted by Pet_Sounds
Yeah, there's a difference in equations. Calculus was invented basically for this question. You need an "open interval" (which can be arbitrarily small) of time around a given point to discuss instantaneous rate of change, and the difference comes down to the behaviour of the object in that open interval as it approaches the point you're interested in. In the case of the ball in mid-air, its motion changes immediately before and after the point in time at which its velocity is zero; the ball on the ground doesn't move at all.
Sorry I'm not explaining this very well, it's hard without math.
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So the "point of non-zero acceleration" is simply a point in whatever relevant bigger equation that relates to the equation that describes the behavior of the object before the "point of non-zero acceleration" and how that relates to the equation describing the behavior of the object after the "point of non-zero acceleration"? [i.e. the ball was thrown (before point of non-zero acceleration), the ball reached its height (point of non-zero acceleration), and the ball fell (after point of non-zero acceleration)].
That sounds like a truism to me, and if that's correct is there an equation or "family" of equations or whatever to describe that "point of non-zero acceleration" or is that point simply a plot to point in the greater equation? Like that point of non-zero acceleration is constant no matter the equation and does not have to be calculated, or the nature of the greater equation of the "rise and fall of the ball" will dictate what the point of non-zero acceleration will be?
Quote:
Originally Posted by Pet_Sounds
Time is what a clock measures.
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But I mean time is a thing we as humans can not measure because we do not have an organ to measure it realistically, in the same way that we use an imperfect two dimensional measuring organ (the eye) to measure three dimensional space. It's not perfect, does not make any sense as a measuring instrument if you look at its performance too closely, but it's good enough for government work. The brain measures time by memory and does so imperfectly but it works as well as we can hope. A clock measures time but we use the brain to interpret what that measurement means and we do it imperfectly which is why we need math to fix our ****.
It sounds to me that this calculus equation you're talking about with nonzero acceleration is our way of breaking down time in relation to a certain instance of movement in a way that makes it make sense in as best a way as we can.