If I'm remembering the details correctly from Jack McDevitt's CHINDI (a novel not related to the TREK universe at all, but just for comparison), the starships in that universe had two types of engines. The normal space engines moved the ship in the way we understand Newtonian physics—action/reaction. The n-space engines also charged up special hyperspace engines. The h-space engines instantly push the ship out of n-space and into hyperspace where speed and duration take on different values. (Basically, the ship must have normal space movement to have any movement within hyperspace.)
The story reveals that if a ship loses mass while in hyperspace, say by dumping cargo overboard, the ship will have greater speed when returning to n-space than when it left. This expose becomes important later in the story when the Earth ship must catch up with an alien vessel that has greater n-space speed than any Earth ship. The Earth ship pushes an asteroid into hyperspace with it, then dumps it there and returns to n-space traveling at a much higher speed.
Of course, this has no bearing on STAR TREK as there are numerous times when the Enterprise
at warp speeds. The technologies in the show are all fictitious, naturally. But if the writers had nailed down details like the above, it might have made some of the stories more interesting.
Also, I don't believe it is necessary for Federation ships to build up any speed with impulse before engaging warp. One example that comes to mind is "The Enterprise Incident," where Kirk zings away from the surrounding Romulans at warp 9. If the Enterprise
had so much as twitched on impulse, the Romulans would have blasted them. (Kirk did the same stunt in "The Deadly Years," but with a really cool reverb. "Warp factor 8, now!")