Depends on what you mean by "bike", and which one you choose.
If "bike" = bicycle:
Some bicycle computers are quite stupid, and will readily accept being programmed with a wheel circumference that wouldn't occur on a regular bicycle. One of these would work with a go kart.
You'd need to find a good place and a good way to mount the magnet, but otherwise, no big deal.
There is a slight risk that the bicycle computer might not be able to accept the speeds a go kart can reach.
If "bike" = motorcycle, it's probably trickier. Motorcycle speedos can have either a direct drive off the front wheel, or an electronic pickup in the gearbox. Either way, they're not as easily reprogrammed as bicycle computers.
A 3rd option is to use something GPS-based. Maybe even a cellphone app. Runkeeper or Strava might work. There are probably similar apps for motorized vehicles that'll do a better job.
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