I don't wan't to go in a big mathematical approach here but more of a kind understand some implications of special relativity.
Since a object from a steady observer is time dilated and length contracted, is the velocity then still the same from the observers perspective? I mean when an object approaching a black hole it will "appear" to slow down when it approaches the event horizon and at a time it will freeze at get red shifted into oblivion. But if it appears to be slowing when the velocity is increasing, would an object accelerated from rest (in your frame), say to 0.6c, actually move with a that velocity when it gets to that speed. If you watch it accelerate with constant acceleration it would not appear as constant acceleration but acceleration which gets a bit slower until it reaches the velocity? That is what i mean by a velocity that is implicit dilated from the consequences of that constant acceleration from a steady observer isn't possible and therefore reaches a velocity that is a bit slower than it should be. Would that imply that an object moving 0.9999c is appearing to move slow? Thank you.