Plug in strip. Mount to cart. Add extension cord.
Why reinvent the wheel?
But hey, if you want to get technical, then yes, you'll need to run a separate GFCI circuit breaker, heavy duty cable rated for portable use, ensure you use cable protection covers/boxes for the exposed cable on the ground, as well as proper outlets on the cart itself. Make sure you use covers on the outlets, mount protective impact barriers around it so it can't be accidentally hit or damaged. You'll want to be running 10 gauge or larger.
All of which will run you around $5-600, be horribly awkward, inconvenient, and a terrible tripping hazard to make sure you never actually use it.
Or just get a plug in strip and extension cord.