title: Solving Acceleration for Time with a limited velocity
body: <p>I'm working on a calculator in Excel for interstellar travel times. I'm currently solving an equation for Acceleration for Time to arrival like so:</p>
  
  <pre><code>=sqrt(distance*2/acceleration)
  </code></pre>
  
  <p>which seems to work fine for me, except that if I give it a large enough acceleration and long enough distance, I get a maximum velocity back that is higher than the speed of light.</p>
  
  <p><strong>What I want to do is add in some limiting factor into the formula that limits the velocity to some number</strong>, but I have no idea how to do this in the mathematics (disclaimer: I'm a writer and artist, so I suck badly at math). I think I need to integrate something like <code>V=min(C,d/t)</code> where C is the speed of light, but I don't know how to integrate that into my function. Since the rest of this works without having to chart out periods of time, I'd prefer a solution in the formula rather than some roundabout recursive chart trickery. Any ideas?</p>