FTL travel might be impossible via acceleration
How do you get from a velocity of "a bit" to a velocity of "a fucking fucking bastard fucking lot" without accelerating?
Well, as velocity is the change of location according to time, not speed which is affected by acceleration, what people are usually saying is that they get from point A to point B in a time faster than light can through a vacuum through Minkowski space (flat space). If you are talking about raw speed, it could be that particles could be created going faster than the speed of light, therefore never need to accelerate. Those would be tachyons and the only real serious talk about them was in a Michael Kaku book saying that somebody figured out they were possible, but only in a universe that was at a false vacuum and this probably happened at the beginning of the universe but such things would cause instability and for the universe to fall to a more stable vacuum state. Beyond that, there is the idea of warping space such as the Alcubierre drive as while the speed of an object through local space cannot get to or go beyond light speed, a section of space can move fast enough for the effect with something inside of it or by shrinking space ahead stepping across and then letting it re-expand. However, space is really, really hard to get to bend even though we know it does, taking planet or sun sized chunks of matter just to do it a little. The other ways such as hyperspace or worm holes are assuming that there is a separate path to where you want to go that is shorter than normal space. In hyperspace it would be other dimensions (such as those string theorists keep talking about) that are still connected to our normal space or drastic bits of Riemannian space (curved space). We can see a similar example of this in gravitational lensing where two paths both follow light like paths to a single point, but one can be shorter than the other. It is also possible that if there are other dimensions, such as possibly where our space and universe was born from, that the laws of physics would be different and there might not even be a lightspeed limit.