In some cases where drivers were allowed to leave after being stopped briefly, there appears to have been no clear motive other than a desire to wield the power of the badge for personal satisfaction, the police said.

In Jackson County, for example, the man who identified himself as a deputy sheriff let the driver of the dump truck go without asking for his ID or demanding any money, Sheriff Mangum said.

She said the police were investigating whether the bogus traffic stop might be linked to at least two similar incidents of police impersonation in Gainesville, Ga., and Dawson County, Ga.

A 2012 study of 56 incidents of police impersonation found that the perpetrators fell into three general categories: Many were “common crooks” looking for a quick shakedown; a few were “cop wannabes” attracted to the authority and ego of policing; and several were driven by “uncommon compulsions” — impersonating officers to engage in sexual misconduct.

Callie Rennison, a professor at the University of Colorado Denver, who helped to conduct the study, said impersonating a police officer was easy because it required little more than a few basic tools of law enforcement like a flashing blue light or a Ford Crown Victoria.

“It all came down to power and control — having those symbols and people obeying it,” she said. “It’s terrible for legitimate police officers because it undermines their authority.”

The police recommend that drivers should call 911 if they fear they’ve been stopped by a bogus law enforcement officer, because dispatchers can determine if the stop is legitimate. They also recommend stopping in a well-lit, public area and turning on the hazard lights to draw the attention of passing motorists. Drivers can also ask to see a badge or an identification card.