Could Captain Kirk's Starship Enterprise Whip Darth Vader's Imperial Star Destroyer?

A Star Destroyer is more than five times longer than Kirk's Enterprise (and two-and-a-half times longer than Picard's Enterprise). So if size is anything to go by, the Enterprise stands little chance in a frontal assault.

However, the Federation has more advanced technology in some respects—notably, transporter technology—and if the Enterprise crew can draw upon their much more extensive mission experience, the situation is much more hopeful.

For example: Kirk, Spock, and McCoy inject themselves with hefty doses of kironide, the chemical that gives psychokinetic powers (Plato's Stepchildren), then transport directly to the bridge of the Star Destroyer to confront Darth Vader on an equal telekinetic footing. They stun Vader with phasers set on wide dispersion so he can't block them with his light saber, then take him back to the Enterprise. Before he wakes up they use the transporter to split Vader into his good and evil halves (The Enemy Within). The evil Vader is kept under sedation while the good one tells them everything they need to know to overthrow the Empire. Then the Enterprise uses a slingshot orbit around the nearest sun in order to go back in time (The Voyage Home, et al.) and prevent the fall of the Old Republic. The End.