Have you ever put your hand outside a car window? I've enjoyed doing that these last few weeks. Something does not slow immediately, just because it leaves whatever accelerated it. The only thing that would make something stop outside of a car is air resistance: which there is none of in space.
In addition, rockets can be seen to accelerate at 28,968 kilometers per hour, and that's with air resistance as a factor. Even if keeping up were an issue (which it isn't) it would be no problem.
I didn't realize just how interesting a topic rockets were, thank you. We don't have them where I'm from.