Of course it doesn't take much imagination to picture the "we're at maximum warp" line coming a day and a half later, after Captain Pike walks onto the bridge after a night's sleep and spends most of the morning reviewing a much more detailed version of Chekov's "mission broadcast."
Does that really make sense to you that someone announces "We're at maximum warp" a day and a half later? And that Chekov makes an announcement to the crew three minutes before they reach their destination after a whole day and a half has already passed by?
The way the entire scene is structured and edited, the trip to Vulcan is so short that as soon as they have reached maximum warp, it takes them only about 4 further minutes to get there. And the shipwide announcement to the crew about what the hell this unplanned mission actually is about can only be done 3 minutes before they arrive.
And I somehow can't see Pike having to spend a lot of time to review a more detailed version to come up with the following three lines.

At twenty-two hundred hours, telemetry detected at an anomaly in the neutral zone, what appeared to be a lightning storm in space.
Soon after, Starfleet received a distress signal from Wulcan High Command that their planet was experiencing seismic actiwity.
Our mission is to assess the condition of Wulcan, and to assist in the ewacuations if necessary.
I'm not sure you noticed this, but Kirk changed his clothes too, before even going to sickbay. McCoy probably talked his way into the quartermaster's office and got him registered as a crewmember.
Yeah, I noticed that, and it's another funny thing. Kirk was already leaking and whatnot, yet McCoy took the time to let him redress instead of taking him right to sickbay, yet he himself did stay in his red cadet suit?

The better question is, how long does it take you to wake up from a mild sedative?
Apparently as long as it takes a starship to accelerate to maximum warp.

Another thing that might support my version is that we see how fast the symptoms of Kirk's various diseases come and go, and that McCoy says to him "Well, those symptoms won't last long." before he becomes unconscious. His swollen hands and numb tongue, for example, come and go in less than two minutes. So the mild sedative might also have been just for like 5 minutes to stop Kirk's whining.
I don't know how long you need to switch clothes, but I don't need more than a minute. So let's say 5 minutes passed altogether. Or 10. 15 minutes to get from Earth to Vulcan. Still a lot less than several hours, and still too short, no?
Too short only if you feel that way and still assuming it took that amount of time.
So you don't think 15 minutes to Vulcan is too short? So what amount of time would you assume? Still hours? Days even?
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