What is the fastest a realistic rocket could go?

[Mr Skeptic]

What's the fastest you figure a realistic rocket could go (must carry a human passenger)? And what basic design would it use?

 

As for realistic, let's say that means it would cost less than 100 trillion including R&D through construction, over several years of course. And if the budget were only 1 trillion, how much slower would it be?

[rktpro]

I think 3 times the speed of sound. For this you have to remove the windows because they might melt..

[StringJunky]

This might be a starting point for finding out:

 

http://en.wikipedia.org/wiki/Project_Orion_(nuclear_propulsion)