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This is something I dreampt up in a physics lab about imagining infinity but I never got round to modeling it. Seems like it could get out of hand pretty quickly!

Imagine we have a ball in a 1d system that bounces back and forth between point x1 and x2. Every time the ball hits either x1 or x2 it reverses direction and doubles speed.

After time t what will be the number of times that x1 will be hit.

Given initial conditions of x2-x1 = 1m and initial postion = x1 and initial speed 1 m/s, how many times will x1 be hit after 5s, 10s, and 20s.

Nikos
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    At t = 2 wouldn't it already have hit x1 an infinite number of times. Since it would take half as much time the total time would be 1 +.5 +.25+.... and that sum converges to 2. – user262291 Feb 29 '16 at 00:38
  • Based on the comment it will be infinity for all... – Moti Feb 29 '16 at 02:18

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