When we say something travels at 50% the speed of light, it's always relative to some inertial, approximately inertial, reference frame, often implied.
So eg. if you hear about the particles at the LHC travelling at near the speed of light, it's implied that's relative to the Earth.
The speed limit comes in here: no-matter what nearby object you look at, its speed relative to you always be less than the speed of light. (Here, nearby means something like "within the local group of galaxies" - objects a long way away can be receding faster than the speed of light due to the expansion of space in between you and the object). You can accelerate as much as you like for as long as you like and when you stop accelerating and check, that'll still be the case.
So eg. if you hear about the particles at the LHC travelling at near the speed of light, it's implied that's relative to the Earth.
The speed limit comes in here: no-matter what nearby object you look at, its speed relative to you always be less than the speed of light. (Here, nearby means something like "within the local group of galaxies" - objects a long way away can be receding faster than the speed of light due to the expansion of space in between you and the object). You can accelerate as much as you like for as long as you like and when you stop accelerating and check, that'll still be the case.