KANSAS CITY, Mo. — A team of computer programmers here set out to learn how many cute kitten photos can 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 and is not exactly a hotbed for tech start-ups, figuring out what you are supposed to do with all that speed 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 cable television and Internet running at one gigabit a second. That is about 100 times as fast as the average connection in the United States (on which it would take about two-and-a-half minutes to download 612 kitten photos).

But be careful what you wish for. After a few million in waived permit fees and granting Google free access to public land, the area is finding out that Google Fiber is so fast, it’s hard to know what to do with it.