This is more realistic. But it begs the question, why didn't the destroyer out-run it? The freighter was approaching from it's back side, and should have given way, but once you realize it's not going to you have 100,000 horsepower to accelerate away with.

And standing orders were to wake the captain whenever another ship gets within a minimum distance. So the watch had to not only decide to play chicken with the freighter, but not wake the captain when it breached minimum safe distance.