Will rockets accelerate until they run out of fuel?

Andrew - In fact, it would just carry on accelerating forever until it ran out of fuel because the reason that it's accelerating is not so much to do with measuring particular speeds. It's more just to do with the fact that it's throwing out lots of mass out of its rear end, to put it nicely, and when it does that, it feels a little push. This is one of Newton's laws - every force must have an equal and opposite force. It receives that equal and opposite force, and as a result, it accelerates.

Chris - This reminds me of a question we had in the Naked Scientists awhile back which was, how hard would you have to pee to push yourself over. I think the answer we've worked out was, you would have to be able to pee and produce a fountain, more than 20 metres high in order to achieve sufficient force that would have any kind of backward propulsion, assuming a modestly weighted man. Similar physics, Different situation.