Wink of an Eye
The U.S.S. Enterprise responds to a distress call from the planet Scalos; the call shows several Scalosians asking for assistance. Arriving at Scalos, however, the crew find only an empty city, with no life forms registering on tricorder scans. Compton, a young, inexperienced crewman samples the local water and disappears.
Beaming back up to the ship, the crew investigates while the U.S.S. Enterprise experiences a series of strange malfunctions. When an alien device is found in engineering, the ship is put on full alert. Back on the Bridge, Kirk sips coffee and suddenly finds himself "accelerated" far beyond the rest of his crew. After acceleration, he is able to see and interact with the missing Scalosians, who are now on his ship.
Kirk meets Deela, the Queen of the Scalosians, who specifically chose Kirk to be her consort. Deela reveals the Scalosians' plan to cryogenically freeze the crew of the ship so that they will have a ready gene pool to integrate into their radiation-contaminated one. Kirk also finds his missing crewman, Compton, and sees the effects of rapid acceleration — any damage to cells causes an accelerated death.
Kirk manages to send a message to Spock and McCoy warning them, and delays the Scalosians long enough for Spock to join Kirk in his accelerated state. Spock brings a possible antidote with him, and after stopping the Scalosians, and returning them to their planet, Kirk takes it. The Captain returns to normal, and Spock uses the advantage of his acceleration to repair several of the ship's systems, before he too returns to normal speed.