P = V*I
P = 3000W
V = 36V
I = P/V = 3000/36 = 831/3A
On 16 AWG wires going to the motor, it will be about a minute before the isolation turns into smoke.
It's probably a e-bike motor. They are undersized for cooling, since you can get them up to speed in seconds, and from humans you cannot really expect more than 3-400W so even 1KW feels like a lot.
Sorry it was a translation error. Its size of bigger rc car, but with no rc. I guesstimate it'll weigh at around 20 kg.
Plan is to have it run on mostly paved flat ground.
Apologies for confusion
Yeah, since would will be using some sort of ESC see what sort of settings you can set up on it is software. You can limit the input or output current or power in the ESC, and size the battery pack based on that. I doubt you will need 3KW, probably 2-300W will provide plenty of acceleration and speed.
As I said, cyclist will use 2-300W peak power, to drive a 80KG person, and go 30-40Km/h easily.