Hmmm . . . Have to ask the resident astronomers here for a complete explanation, but all asteroids definitely do not travel at the same speed relative to Earth, though I think there are correlations between their speeds and their origin. For instance, asteroids coming in from the asteroid belt between Mars and Jupiter come in relatively slowly (though God help us if a big one ever smacks into us!), whereas asteroids and comets coming in from further out in the solar system, or even interstellar space, tend to be moving quite a bit faster.
I think that there is much discussion that could be had on this topic.
I'm not a physicist, astronomer or rocket scientist...but this subject as both intrigued and concerned me for years.
Aren't "falling stars" after all, just asteroids and comets on near misses of Earth?