[vonmoltke]

A constant acceleration of 1g would cause the ship to hit c in about one ship year.

[Thrymr]

The ship will never hit c.

[nealabq]

If the ship travels tens of billions of light years will it eventually be traveling away from it's starting point at greater than c due to the dark-energy expansion of space itself? Or will the ship just red-shift more and more but never disappear from an observer with a very good telescope who stayed home?

And what if you drove your ship straight into a super-massive black hole?

[isostatic]

One theory of the far future (Big Rip) is eventually nearby galaxies will be receeding faster then light, then stars, planets, then even atoms.

There's a short story about the Big Rip

https://web.archive.org/web/20080725045740/http://www.solari...