Motor calculations for go-cart / go-kart
You can use ramp medel and required climb-up velocity.
For example you need to climb 15-degree ramp at 4m/s and you cart is about 100kg.
So it equivalent lifting up 100kg mass at speed 4sin(15 deg) = about 1.04 m/4 so you required mgh/t or mg*v power. Then you got 100 * 9.81 * 1.04 = 1020.24 watt of mechanical power. (don't forget to consider efficiency of motor to convert electrical energy to mechanical energy).
If you planned to use DC motor you need to know torque-speed curve of DC motor

(Image credit: National Instruments Corporation)
At 50% of noload-speed, the motor will provide maximum power, so you can design gear reduction to make motor turn at 50% of no-load speed when climbing the ramp.
There are no absolute way to select motor. there are to many unknown factor such as air resistance or mechanical friction. this calculation will give some guild line and you need to do some experiment to verify and adjust some setting.