Also, rule of thumb, to double speed, quadruple power.
Actually when you double speed resistance losses quadruple and you need 8x's (2e3) the power.
Speed only accounts for 2 dimensions.......distance/time
Power is a measure of work performed in a given time or for those academically inclined force x distance /time. 3 dimensions.
In a balanced system friction losses will equal acceleration forces giving you a vehicle traveling at a steady speed which only requires a certain amount of power. Let's assume your kart has 4 (2x2) square feet of surface area directly opposed to wind. To double your speed your kart will be pushing that air twice as fast effectively doubling the dimensions of your exposed area (4x4 or 16 sq ft). So comparatively your area increased by a power of 2.
Power=force x distance / time
or
power=force x speed
so therefore if force (wind resistance) raises by a power of 2 and speed increases by a power of 1 (doubles) you add the exponents and reach the solution that power required is cubed. In this case. It would be 2 raised to the 3rd power or 2x2x2 which is 8.
Think about a NASCAR with 800 hp that tops out at 200 mph and compare that to a family car that uses maybe 100 hp to go 100mph.