To figure out how much power you will lose and speed you will gain, divide the radius of the tire by the radius of your rear sprocket. Take this and multiply it by your gear ratio. This is your effective gear ratio putting power to the road.
So, if you have a 15" tire with a 7.5" sprocket (just for example), and your gear ratio is 6:1, your effective gear ratio will be 3:1 when putting rubber to road. So, if you engine puts out 10 ft*lbs of torque and the above, you will be putting 30ft*lbs of torque to the road.
One ft*lbs is the force of gravity acting on a one pound object and is 32ft/s^2 of acceleration. You take your torque and divide it by your total weight then multiply by 32. This will tell you your acceleration.
So in the above example with 30ft*lbs of torque. If the total kart weight is say, 300 lbs, this will give us .1 foot, times by 32, and you get 3.2 feet per second.
So, with the above configuration, you will be going 3.2 fps faster each second until you reach maximum speed.
I THINK that what I have stated here is correct. So, in 10 seconds of time, you will be going 32fps, or 21mph.
The only part I am unsure of is calculating acceleration from ft*lbs, I've only ever used Newtons.