Kirk orders "Impulse
power, Mr. Sulu. Ahead warp point five." This is a very
intriguing order. He is, after this, concerned about engaging warp drive
within the solar system. Ordered to warp one, Sulu gives a count off
through .7, .8,, .9 and then finally warp one. Running into a wormhole,
it will take 22.5 seconds to brake to sublight. This is echoed in STVIII
with some changes; the Pheonix is using its warp drive while accelerating to light speed.
STV: The planet Nimbus III is fairly close to Earth, as indicated by the Enterprise being one of the closest Federation vessels while in Earth orbit. Earth being 25,000-28,000 light years from the galactic core, the 6.7 hour trip at warp 7 indicates a speed between 32-38 million c.
STVII: The Enterprise-B has a new inertial guidance system.