This is easy to google (I should have done so before) but still hard to believe. If that's peak speed for only a short time because of fuel limits, it's less hard to believe.
...what do you mean by "peak speed for only a short time because of fuel limits?" It's space. You don't need fuel to maintain speed. What's going to slow you down?
Oh: To clarify, "Escape velocity" is the speed you need to escape Earth's gravity well entirely, so that you are no longer orbiting the Earth at all; it's about the amount of velocity you need to go on interplanetary missions. If you just want to go to, say, the Moon, then you don't need to go that fast. If you just want to go to low Earth orbit (LEO), then orbital velocity's only around 7 km/s.
But that isn't "peak speed" or anything, that's just ... how fast you have to go to be in low Earth orbit. The International Space Station is traveling at 7.67 km/s right now.
However, I did actually mean to type km/s. Earth's escape velocity is, in fact, 11.2 kilometers per second. (Around 25,000 mph)