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Ok... For silly reasons, I'm on the FLAT EARTH forums polishing my debate skills...
I'm actually having some fun... these people are serious nuts... heh. Anyway, This guy posited a 'proof' demonstrating his assertion is that a particle can accelerate forever without exceeding the speed of light. Here is his proof:
Proof. Consider a particle moving along a line so that its speed as measured by observer A at time t is given by v(t) = c-c/t. Initially, the particle is at rest with respect to A. The derivative of v(t) is c/t^2, so the function c-c/t is always increasing, so the particle is always accelerating. However, this function will never be greater than c, since for t>0, 0 < c/t < c. Thus, the particle will never be moving faster than light, but will be accelerating forever.
Here is my reply:
How is observer A relevant at all?
What, you think I'm an idiot? the definitive equasion (t>0, 0 < c/t < c) is not related to the velocity at all. In addition, c/t can't be higher than c unless time is negative.
Nice try, dumbass.
Analysis please. Did I miss something?
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