With e-bikes soaring in popularity, regulators have been unable to keep up with the quickly-evolving market. Safety and law enforcement officials note that many models marketed to children and teenagers exceed legal speed limits and more closely resemble motor vehicles, which require a license and registration to operate.

For the moment, the power to decide what teenagers may or may not ride falls to a nongovernmental authority: parents. Across the country, they are expressing a mix of enthusiasm, contrition and uncertainty about the trendy mode of transportation.

Some parents who initially embraced e-bikes now say their enthusiasm has waned with news of recent crashes involving teenagers.

“Initially, it was a godsend,” said Julie Wood, whose daughter Sawyer, 14, got an e-bike this past spring. “She’s a teen — she wants to go everywhere.”

For Ms. Wood of Boulder, Colo., that meant less time carting Sawyer in the car. But she had a firm rule that Sawyer wear a helmet.

In early August, Sawyer crashed while riding her e-bike without a helmet. She did not tell her mother, fearing disciplinary repercussions, even though she was experiencing headaches and nausea and did not want to get out of bed. Several days after the crash, she had a seizure and underwent emergency brain surgery for a skull fracture and a brain bleed; she is expected to recover.

Her mother is now rethinking how society should handle the technology. “These kids don’t have driver’s licenses,” Ms. Wood said. “As much as you want to believe they are riding a bike, it’s just different. They go really fast.”

After news of Sawyer’s accident spread around town, Scott Weiss, a Boulder resident and parent of two teenagers, decided to sell the family’s two e-bikes. “I want to keep you alive as long as possible,” he told his 14-year-old daughter. He said he would sell the e-bikes only to someone “college-age” or older: “I don’t want to sell it to someone who is not prepared to make the mental judgments you have to make.”

The questions around e-bikes fit squarely into a modern theme in which powerful technologies, like mobile phones and vape pens, enter the market and are sold directly to consumers, without much research available on the impact on behavior and safety.

In the case of e-bikes, some models can be reprogrammed to exceed the 20-mile-per-hour speed limit permitted for riders under 16; they therefore fall into the category of motor vehicles. The federal government has not yet figured out how best to regulate them.

That is just fine with some parents who say that the decision about whether to let a child ride an e-bike should be made by an individual family and be based on whether a teenager is able to handle the roads and speeds.

“I know my son and I know his athletic ability,” said one Southern California mother, who asked that her name not be used because she felt that her views might draw criticism. Her son has two e-bikes, a Super73 he got for his 13th birthday and a Talaria he got for his 14th birthday. “He lives on two wheels,” his mother said, adding that the e-bikes were a source of fun for him.

The teenager has modified each of the bikes to go faster than he is legally allowed to ride them; in fact, the Talaria can hit 70 miles per hour. His mother gave him her blessing, she said, and even helped him clip a wire that removes the speed “governor” that ordinarily limits the vehicle to 20 miles per hour.

She posited that the companies designed the bikes to allow the speed caps to be removed. “They want you to be in charge of doing it,” she said, “because they don’t want to be held liable producing a bike that goes 55 miles per hour where a kid goes straight into the concrete.”

Gari Hewitt, a nurse in the area and a friend of the mother’s, expressed more caution about e-bikes. Not long ago, she saw a 12-year-old boy lying unconscious in the street. He had been riding a Super73 when he hit a rock and “flew over the handlebars,” said Ms. Hewitt, who works as a nurse in a pediatric trauma unit. She checked out the boy before he was sent to the hospital; she later learned that he had a punctured lung, among other injuries.

Ms. Hewitt has two teenagers of her own, a 15-year-old girl and a 14-year-old boy. Each received an e-bike for Christmas. “When they’re this age, how do you wow them?” Ms. Hewitt asked. “We only have a couple of years left to wow them.”

The e-bikes came with rules: Always wear a helmet, don’t exceed 20 miles an hour, never ride at night. The hospital where she works considers any crash at speeds of 20 miles per hour or greater to be “a trauma activation,” she said.

“But you could hurt yourself on a bike, too,” she said. “Everything comes with responsibility.”