Well, I don't know, but when I used Google, I didn't come up with anything directly, but this:

Quote:

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Astronauts use a centrifuge to simulate the acceleration of a rocket launch. The centrifuge takes 20.0 s to speed up from rest to its top speed of 1 rotation every 1.40 s. The astronaut is strapped into a seat 7.80 m from the axis.

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From this, you can work out the speed which happens to be:



Hm... that's not much.

Maybe you're looking for the acceleration astronauts can withstand?



This is about 16 times the acceleration due to gravity!

Since you asked about speed, and not acceleration, you should understand that speed is relative. There are no issues with respect to what a person can "withstand" regarding one's speed relative to another. It's change in speed, or acceleration, that is an issue, as Unk described. But as for some speed records:

1. The speed with which astronauts returning from the moon as measured relative to the earth is max about 40000Km/Hr, or 11.1 Km/s.

2. The earth orbits around the sun at about 30 Km/s.

3. The solar system moves through the Milky Way Galaxy at about 220 Km/s.

4. The relative velocity between galaxies can vary quite a bit, but astronomers have observed that we are moving at a speed of about 75,000 Km/s relative to the most distant observed galaxies.

So there you go - you yourself are moving at 75000 Km/s as measured by someone on that distant galaxy - yet you have no issue "withstanding" that at all! The only true limit is that nothing can move faster than the speed of light, or 300,000 Km/s.