I don't know the name of this problem, but I heard it some time ago. The statement was if a planet is distance $d$ away, and you know both the current maximum velocity of spaceships $v_0$ and the growth rate of spaceship propulsion technology $a$ (so that $v(t) = v_0 + at$), when is the optimal time to send a spaceship to the planet (assuming, of course, that once a spaceship leaves, it's velocity is fixed and cannot be increased by the technology on Earth)? This problem can be applied to many situations such as the Business or Accounting fields, so I feel as though there should be a name for this problem.

Note: There's also an application to the "Cookie Clicker" game. Perhaps this question would get more answers on the gaming SE?



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