KANSAS CITY, Mo. » A team of computer programmers here set out to learn how many cute kitten photos could be downloaded in one second on their Internet network, one of the fastest in the country.

The answer: 612.

A trivial pursuit? Perhaps. But when your city has Internet capacity to spare, figuring out what to do with it is a challenge.

It has been a little more than three years since the Kansas Cities — both Kansas and Missouri — won a national competition to be the first places to get Google Fiber, a fiber-optic network that includes television and Internet running at 1 gigabit a second. That is about 100 times as fast as the average broadband connection in the United States (on which it would take about 2 1/2 minutes to download 612 kitten photos).

Google Fiber is so fast, it’s hard to know what to do with it. There aren’t really any applications that fully take advantage of Google Fiber’s speed, at least not for ordinary people. And since only a few cities have such fast Internet access, tech companies aren’t clamoring to build things for fiber. So it has fallen to locals — academics, residents, programmers and business owners — to make the best of it.

"I wish there was one thing where I could be like ‘Dude, get ready, this thing is going to blow your mind,’" said Matthew Marcus, co-founder of the Kansas City Startup Village. "But there isn’t yet."

Still, while there isn’t yet a killer app, it isn’t for lack of trying. Ideas have ranged from installing fiber-connected cameras in high-crime areas to building a model home where entrepreneurs could test Internet-connected appliances.

The average connection speed in the United States is about 10 megabits per second, good for 14th in the world, according to the Internet company Akamai Technologies. That was Google’s impetus for starting Fiber, which has expanded to Provo, Utah, and Austin, Texas.

The company is in discussions with nine other metro areas, including Atlanta, Phoenix and Portland, Oregon. (Chattanooga, Tennessee, and several other cities have fiber networks of their own.)

Kevin Lo, the general manager of Google Fiber, said the Internet giant had plenty of patience to see what percolated in the cities with its high-speed network.

“We need to encourage developers who have great ideas, but we also need to build a critical mass of people who can use those applications. You need both for the breakthroughs to happen,” he wrote in an email.

© 2014 The New York Times Company