If you push a ball in space it will eternally fly in the speed you started - theoretically. Only other things will slow it down. An asteoride may be part of a former explosion or collition in space and got thrown into space by huge forces. They will fly eternally that way only slowed down by possible gravity of of plantets or if they collide with something. Little particles may slow it down a bit, but larger ones will stop it - e.g. if it collides with a planet.
If the planets needed jet propulsion or any other means for speed they would fall into the sun as there is nothing of this kind available. Thus, a moon thrown into space by a huge force may fly into our solar system at a good angle to get into an ellipse around the sun. If it is not too fast it will not be thrown off again. If it is not too slow, it will not get closer and closer to the sun and not be swallowed by it. Another little planet in our solar system may have arrived. If the speed is correct (ideal) it will fly its round near to eternally - as to human feelings. Just theoretical.
Theoretically a friend could kick you in the a... and you might fly all the way from Los Angeles to NY without any engine. But two things will stop you here. The gravity of the earth will draw you to the ground and second the air will hinder your flight and you'll get slower and slower. Without these two powers you may fly to NY in this way.... theoretically for as you'd fly staight and the earth being round you would rather fly off the earth. ;) That's the problem with theory.
Say an asteroid it traveling at 1000 MPH as it get closer to a planet the gravity pulls on the asteroid increasing it's speed to say 2500 MPH if the asteroid misses the planet it will change trajectory and veer off into space. The asteroid will maintain about 3/4 of it's additional speed that it gained.
Fro each time it passes a planet that pulls on it it keeps gaining speed in this way. After it passes so many planets it can reach speeds of more than 50,000 MPH.
NASA uses the same to gain speed of it's deep space crafts.
It's call the SLING SHOT. affect.
Actually they travel much slower than the earth.
The problem is the gravity of earth, if one falls on the earth it will accelerate to a terminal velocity of 25000 mph before it hits.
To make it worse the earth is traveling at 66000 mph so if it is a head-on collision the approach speed will be 66 +25 = 91000 mph. (devastating)
All bodies in Solar system have orbital speeds governed by Kepler's laws. It applies to movement of Asteroids also.
As a rule of thumb (if you stretch Kepler's third law a bit) the average speed is inversely proportional to its average distance 'a' called semi-major axis.
Comets mostly, Asteroids, TNOs & Objects in the extended disc have high eccentricity orbits with their Perihelions (at their least), grazing past Earth's orbit. At that distance (whose value is 'a(1- e)' ) the speed increases several fold making it appear moving extremely fast.
As a crude estimate an Asteroid in its belt at an average distance of 28 AU, can be expected to have a speed (average) of 1 km/s (derived from Earth's average of 29.87 km/s). A grazing Asteroid with a Perihelion of (28 -1) has 'e' given by
(28 -1) = 28(1 -e)
=> e = 0.036
and speed (my crude estimate) nearer to Earth's value. The relative velocity is the result of the difference to all the way to added (if the orbital elements of it are opposite) value of velocities (about 57 km/s).
It depends on what you're comparing the speed to. You knew that the Earth travels REALLY fast in space, right? Like 30 kilometers every second? That's because it is in orbit around the Sun, and if it slowed down it would actually fall into the Sun instead of going around it.
So, if an asteroid was travelling beside the Earth, it would also be going 30 kilometers per second (kps), but would look like it was stationary to us.
Or if it was travelling in the opposite direction at 30 kps, we'd see it as though it was travelling at 60 kps!
Also, there's no air in space to slow the asteroid down. The only reason an asteroid would change speed would be if it hit something, or it got close to something bigger and got faster as it fell towards it due to gravity. If it didn't actually hit that bigger object, as it went further away it would slow down again as it was dragged back.
So your possible answers are:
1) It got hit by something else, that sped it up; or
2) It accelerated due to gravity.