Right, they jump to warp, time passes (where things like Kirk coming out of his drug-induced coma and McCoy changing his clothes occur) and then Chekov does his ship-wide annoucement that they'll arrive in Vulcan in a five mnutes.
Well in my memory Sulu manages to get the ship to warp and then before the camera even leaves the bridge someone says the 4 point something line. I'll concede on this one when I re-watch the film.
I just watched the bit.
It's Chekov that says they'll arrive at Vulcan within 3 minutes during his announcement.
Which means... Trekker4747, that it takes 3 minutes for Kirk to wake up and arrive at the bridge.
This is the exact sequence of events:
1. Enterprise goes to warp
2. McCoy and Kirk arrive in medical bay, no doubt minutes after ship leaves Earth orbit. McCoy wearing red cadets uniform
3. "Engines at max warp" -Sulu (again, no doubt a few moments after entering warp)
4. Chekov makes mission announcement.
5. "We should be arriving at Wulkan within 3 minutes, thank you for your time" - Chekov
6. Kirk hears announcement, and rushes to bridge. McCoy changed into blue uniform.
7. Enterprise exits warp at Vulcan.
Obviously a bit of time needs to pass for McCoy to change uniform, but I don't think it's that long.
So either:
1. Ship takes hours to reach Vulcan, Kirk is unconscious for hours, mission announcement takes place minutes before arrival, engines take hours to reach maximum warp.
or
3. Ship takes 15 or so minutes to reach Vulcan, Kirk is unconscious for most of that time and is awoken by Chekov's announcement recently after going to warp.