Do peace officers really have the power to commandeer private vehicles?

We’ve all seen television shows and movies where some policeman or federal officer demands someone allow them to use their personal vehicle. A reckless chase generally follows where a $50,000 classic Mustang is smashed to bits.
But has anyone really heard of someone having their car commandeered? Wouldn’t this be a violation of the fourth amendment? I’m guessing that it’s just some folktale that’s been told to us by Hollywood, like the false belief that a ship’s captain can marry on the high seas. Am I right? I figure someone out there either is or knows somebody who is in law enforcement.