I'm not a qualified electrician, but I did wire my 220 outlets in my garage for their purpose.
All it took was two 50a breakers, some wire, and outlets.
Now, inside the welder, are little transformers and other magic, that make the amps go far higher than what comes out of the outlet. My welder can weld up to 180 amps. My old HF flux core could do 90 amps. 40 amps, coming off the welder, isn't squat. Even my crappy Home Improvement store special gate took 70 amps to weld up.
Stick welding isn't really the way I'd go on a kart... But since it's what you have, what welder and rods are you using?