How do meteorites pick up speed in space?
They pick up speed by coming near larger objects such as planets and moons. They pick up speed by what is called the "slingshot effect". They are going so fast (velocity) near an object that is attracting them that their speed overcomes the attraction. When the speed overcomes attraction then this has the affect of slinging them.
Meteorites originate as asteroids from space. They are loose rocks that have been formed in the pre-planetary era or have been chipped off of a larger body such as a planet or moon by impact. When they encounter Earth's atmosphere they become meteroids, when they light up due to friction they become meteors, when they impact Earth's surface, they are meteorites.
Space rocks floating through the sky are called meteoroids. When they are passing through the Earth's atmosphere and are heated to incandescence, they are called "meteors". If they crash to Earth, they are called "meteorites". Not all meteors survive to become meteorites. Many meteors burn up completely in the Earth's atmosphere.