The impulse drive has a low level static warp bubble and it works at sub light speeds. It is what allows the impulse drive to go faster than a normal fusion rocket. It is a kind of space distortion, the use of a low level warp field helps the impulse drive avoid inertia. Without kinetic or mass energy build up there is no momentum or any inertia. It is a space distortion that produces a gravity shield. You do not have to go light speed for this to work.
A low level warp field allows the impulse drive to go faster with less energy output and can go from a stop to max impulse speed with in a very short time with no g-force effects and no time delay from relativity. The propulsion is high energy plasma going through the impulse manifold. Unlike the warp drive propulsion is not from space time distortions. The low level warp field stops the relativity and inertia effects, but takes a lot less energy than the warp drive. At first this was done with subspace emitters then later the plasma went through a drive coil before exiting the impulse manifold. The drive coil produced a low level warp field from the plasma.
I have been told that in the star fleet manual it is suggested for ships not to go past 0.5C at impulse. I look at the shows than Theoretical physics in the fields described on the shows. I very seldom look at the star fleet manuals. The writers consult the scientific community on how to make the shows look real, but do not always get it correct. According to general relativity all matter moves in time space and all space time and gravity is connected. To a point this has been proven using an atomic clock, time shows down in a jet to a very small degree. The ship that went to the moon time had slowed down by a few minutes. The GPS everyone uses today has a program that accounts for the differed rate in time of the satellites and the GPS. Time in space moves faster than on earth to a very small degree, but it is enough to throw the GPS off. Now time slows to movement on an exponential curve but at 0.5C it would be large enough to produce noticeable effects. Gravity affects Relativity, mass produce gravity or a mass less gravitational field. Without this you cannot go to half light speed in less than a second. The storylines shows the ships doing this.
On star trek a sub space bubble alters the effects of Relativity like the branes in M- theory. In Real warp theory using a false vacuum state is 1 warp metric that is believed to produce the effects of the branes which allows light or energy to move faster than light in normal space and the lowering of inertia or faster energy drop-offs. This is all connected it changes the effects of relativity.