Beau above has given you some excellent advice based on real life experience. A 250w motor isn't very powerful so be careful with your aerodynamics and weight or consider using two motors - they will take a current/power proportional to the load put on them so running two motors at a vehicle speed of 8mph will not be that much more power consumption than running one of them.
Maybe try it with one, keep the fact that you might need a second motor in the back of your mind and design your kart with the option of a second motor.
I work in the automotive industry and we've seen some interesting stuff through our doors including a design by one of the world leading designers in motor technology - fascinating bloke.
A 250w 24v motor run from 2 x 12AH 12V batteries will run for approximately an hour but pick your batteries carefully as a lot of the lead acid batteries don't like being discharged too much.
If your course is nice and flat, your weight isn't as much of a hindrance as if you have lots of slopes. Once you get up to speed, your only major power drains are your rolling resistance and air resistance. If your course is not flat, consider using some kind of energy recovery system in your controller design.
Good luck