According to the sound effects. This effects indicate a power build up time frame. Furthermore in particular the episode 'Tomorrow is Yesterday' plus the episode 'The Changeling' show that the warp engines can be destroyed energized, requiring time to energize.According to WHAT?!?
And the Galaxy class from Vonda's Wrath of Khan was from two years before TSFS pulled transwarp out of its butt.
In other words a hybrid power train.
This definitely shows that the matter/antimatter reactors don't put out a great deal of power. At least in terms of 'acceleration'* both sunlight and warp.
Keeping in mind that the reactors only have to sustain warp factor six.
This power train has been demonstrated numerous times in TOS.
In TMoST it mentioned that the Enterprise can only sustain deflector shields at optimum power for twenty hours.



