I'm under the impression that the ship to ship battles take place miles apart.
A few thousand meters would be a few kilometers, and 1 mile is about 1.6km.
In any case, fast things on TV seem to move astonishingly slowly, like a laser blast that crosses a room at about the speed of sound.
Did they really slow down or was the enemy simply able to continue accelerating?
The example I'm thinking of was when the Daedalus was being pursued by some alien fighters in "The Daedalus Variations." All of them had their engines at full power; the Daedalus was barely managing to stay ahead of the fighters, but then it suddenly lost engine power. On-screen, it immediately slowed to a stop, and the aliens caught up quickly.
Star Trek is just as guilty - engines fail, and the ship comes to a halt, except when momentum is convenient for the plot. What sucks about it is that, working as an engineer, people seem to have the idea that the laws of physics are actually
very malleable.
"I can't do it in 5 hours, the laws of physics simply won't allow it."
"I need it to happen in the next 4 minutes."
"Ok, fine, I guess it'll be ok, but just this one time!"