The hero vessel retreated from the Romulans at "emergency warp" for at least a minute (the time we saw on screen) and probably two (the estimate Sulu gave), without slowing down or flying in circles. That gives the two vessels a hefty separation, certainly in excess of one lightsecond.
Kirk then gives chase to the Romulans at less than maximum warp, again becoming a sensor ghost to them. He may have closed some of that distance there, but not down to a lightsecond, it seems - because he then orders maximum warp to catch the Romulans before they cross the Neutral Zone border, definitely much faster than the speed of the Romulans, and still fails to appreciably decrease range within the next twenty seconds of action (which involves phaser fire fired from a distance Stiles increduously considers "this distance?").
The main argument for a distance greater than one lightsecond is that Kirk doesn't overshoot the Romulans while firing, despite maintaining maximum warp. Luckily for us, his earlier retreat at maximum warp allows for that.
Timo Saloniemi
IIRC, the book The Making of Star Trek stated that the phasers had a 300,000 km range.
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