What is the fastest speed a human can reach?
The answer is a bit “tricky” because the concept of something’s speed has meaning only in relation to something else.
Anyway, considering future developments, the highest theoretical speed that a person can reach in relation to any other object is “almost” the speed of light. Simply because the laws of nature do not allow a faster speed. This answer also has a kind of “twist” when we’re talking about distortions of space, because the limitation on the speed of light is relative to space and not of space itself. However, here we move into somewhat complex issues.
The practical speed that a person has reached with the help of tools in relation to Earth is about 11 km per second (about 7 miles per second), inside spacecrafts that reached the moon for example. The practical speed reached by a person without the help of tools – in relation to the Earth – is about 50 m per second (about 160 feet per second) during free fall in air. Without the help of tools on the surface of Earth (that is by running) we have reached about 10 m per second (about 33 feet per second).
If we relate to other objects, the speeds become much greater. A person on the equator rotates around the center of Earth at a speed of about half a kilometer per second (about 1600 feet per second). Our entire Planet Earth (with all humans on it) rotates around the Sun at a speed of about 30 kilometers per second (about 19 miles per second). The entire solar system, with humans in it, revolves around the center of the galaxy at a speed of about 230 km per second (about 140 miles per second). Our entire Milky Way galaxy races towards the Andromeda galaxy at rates measured by about 100 km per second (about 60 miles per second).
Note however that if the world is only about 6,000 years old, we don’t actually see most of this. We can only see light (and therefore objects) from about 6,000 light years away – that is only the very near neighborhood of only our own galaxy, out of the trillions of galaxies out there.