And the saucer must have been flying at warp speed in one episode, and supposed to accelerate to warp speed in another. Which is why we know the warp drive is there - we were smacked in the face with it, twice.
Bzzt. Wrong.
TMP showed us full impulse could reach speeds of 1/3c.
You could be outside a star system and get to it in hardly any time at
this speed of impulse. We also don't really know how much time passed to get back to the saucer section. Could've been days for all we know.
I'm guessing the next 100 years of engine designs upped that maximum impulse speed, but in TNG you could go only 1,000,000 km in 3 minutes at 3/4 impulse (33,333,333 km per minute/.75= 44,444,444km/hr or .04c at full impulse).
Let's just assume that TNG reference is wrong because it doesn't fit what I'm trying to say...which seems to be perfectly ok. Why would 100 years of engine design make an engine go 1/10 as fast? Why would a ship of any size have three speeds? Barely moving, sorta barely moving, and then faster than light)
Even warp factors are all over the place. Sometimes you can warp in a system, unless you can't. Sometimes you can turn at warp, unless you can't. What does this mean?
The only speed that matters is the speed of the plot.
The speed of this plot.
supposed to accelerate to warp speed in another
What episode was this?
There was no episode of TNG where a sub-light traveling saucer section accelerated to warp. Nor was there any indication of distance traveled by said saucer section.
Nor has there been any reference to a warp system in the Galaxy Class saucer section - either on screen in dialogue, on the MSD, or in any of the official and countless off screen technical schematics.
There seems to be an assumption that there were vast distances needed to travel, but it could just as easily be assumed that the saucer section dropped out of warp and then by some sort of wizardry became invisible to sensors thanks to the
hyperbolaric plasmotic enducer reduction assembly located on deck 8 (just aft of where the whale lounge was).