1,000 watts, 36V enough for Electric Kart?

I'm looking into building an electric kart and am wondering if 1,000 watts of motor power with a 36V scooter motor is enough power to move a 200lb kart and 200lb rider at 20-30MPH when geared properly. To reach full speed quickly and not struggle to accelerate?

2500 RPM motor geared to a 3:1 or 4:1 ratio
1000 Watts total power
36 Volts
10" dia tires

Thanks.

What if the if the ratio when to 5:1 with 1,500 watts. I hoping to build an inexpensive, small 6x6 amfibious kart that is driven by electric motors on batteries with a small gas motor to recharge the batteries/power the kart. Water-tite body, external drop down chain drive, independent suspension, trolling motor water propulsion. The idea is to use it at paintballs games and parades.

Without any mechanical losses due to any reason, weight, wind , friction, etc.. the theoretical speed at 3:1 is 24.7 mph and at 4:1 is 18.6 mph. As Roy says you've only got a little over 1 hp (1.33 to be more accurate) so it might take a while to get up to speed and only work on flat terrain, or down hill.

1000 watts will give about one horsepower 760 Watts per horsepower less losses. It won't be a ball of fire but just remember a wheelchair/scooter has only only a 250 Watt motor.
Also an electric motor gives maximum torque for acceleration at zero revs and falls off in power output as it gets faster.
RoyS