See this thread:
http://motorbicycling.com/showthread.php?t=4820
http://jimsitton.net/ratiocalc/
The bottom of the three downloads ratiocalc uses engine rpm, clutch teeth number, and (IF you use a jackshaft those input output gears teeth numbers) tires diameter size, you get speed.
Note that other factors are not included that will affect the speed, but to find a calculator that is more involved with horsepower, torque, friction...ect this is something yet to come across and understand fully.
Is that 26 inch rear drive wheel and no jack shaft?
Since I guess the 31 teeth you mention to be smaller than whatever is the go-kart sprocket that is on there now, I just make some quick estimates.
You can also instead of teeth count use diameter for either pulley or gear measuring diameter furthest point to point.
I say 2inch dia for clutch and 10 inch dia for sprocket (not the 31 teeth one not shown). That is gearing down by ratio 10 / 2 = 5 or 5:1 ratio.
The calculator does this and the next part I know the steps but to do this the calculator does it just the same quicker.
Note I see the centrifugal clutch and I am guessing clutch engine idle speed with the Briggs 5hp can idle OK at 1750 rpm and it won’t be engaging the clutch until starting at 2000 rpm and fully engaged the clutch at 2200 rpm.
What this means with the 26 inch wheel at 2200 rpm when clutch is fully engaged and should not be slipping, the speed is 35mph. At a maximum rpm of engine maybe 3500 rpm 54.1mph.
Note these speeds which would be less for the other factors not taken into account, but still useful.
My thinking here is that there is way too little gearing down. Speed of 15 mph starting at clutch fully engaged at 2200 rpm on my 3hp Briggs motor bike was bogging it down to get started I will be using a ratio of 20:1 for dirt biking and a 40:1 for parade speeds most people not going to be using, but I made my system able to switch between the two ratios.
Just so you get an idea of how the use of the go-cart went was 10 inch sprocket and a wheel on the go-kart being practically the same size as the sprocket say 12 inches wheel. The numbers come out as 2200 rpm equate to 15.7 mph and 3500 rpm equates to 25 mph. Going with the same sort of speed range with a similar vehicle weight and engine horse power see below what I think can be done.
What would equate to the 2200 rpm speed equating to near 15.7 mph on a 26 inch wheel the ratio of 5:1 would have to change and be greater like a 10:1 ratio.
10:1 ratio gets 2200 rpm going 17 mph and max at 3500 rpm 27.1 mph. This is I think realistic with a 5hp Briggs.
A jack shaft with like a 2 inch and a 4 inch makes a ratio of 2:1. You then multiply both ratios 5 times 2 equaling 10:1 ratio. You have it.
Just what I think, but see the calculator and try some actual numbers to see what you can find.
MT