Ok, but before you start ordering parts, let me ask you a few questions.
How do you know your cart can go 60mph and not break apart?
Can your suspension and tires take the speed?
Also, if it were me, before I bought any parts I would reverse engineer from the wheels up.
Kind of like this. I would figure out the circumference of the wheels you are going to use and then calculate how many rpm's they will need to get you moving 60mph. Then I would think about gearing and what you are going to need to get the appropriate rpm to the wheel. Once you know how fast the gears must spin then you can calculate the rpm needed from a motor.
Also, look around at electric scooter and motorcycle motors so you can best decide your course of action.
Edit: As an example, and somebody please check my math....
You must cover 1 mile in 1 minute to go 60mph
There are 5280 feet per mile divided by 12 inches = 63360 inches per mile.
A 6 inch wheel has a circumference of 18.84956 inches.
63360 inches divided by 18.84956 = 3361.3516 RPM to cover the required distance in one minute.
However, you will need gears to get you moving (Unless you are going direct drive) and those gears may or may not need to spin at 3362 rpm to get the 3362 rpm to the wheel.
Favorite Quote: "This is L.A., sugar. There is no 'over the top." --- Chris Erskine
Current build: Liahona w/ cheap front suspension and suspension seat post. Yescomusa 36v 800w generic front hub motor. 15ah Headway triangle mounted pack. Tronsung 30 amp,
Previous Build:1992 Trek Antelope 800 - Bone Crusher (no suspension) - Yescomusa 800 watt 36 volt front wheel kit. Don't do it! Get suspension!!!