Electric go kart power train design

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I'm to design the power train of a electric go kart for a competition. I'm having problems with numbers.(considering vehicle dynamics like air drag, rolling restiance)

Competition rules and restrictions on power tarin :
Max motor rating :2500w
Max battery ratings: 48v 35ah
Max system current:60a

What I'm trying to achieve :
Speed of 40-60kmph(I know 60kmph is probably far fetched with even 2500w motor)

Total runtime of 75minutes

Acceleration of 0.8-1m/s^2

Assumptions:
Kart weight: 180kg (if lead acid batteries)
Rolling resistance: 0. 01
Coeff of drag:0. 88 (not sure about this no)
frontal area of kart:1. 19m^2 (not sure about this either)
Radius of wheels: 0. 14m

*feel free to recommend appropriate numbers for coeff of drag and frontal area

Help me arrive at the required motor and battery spec. I arrived at the following numbers:

8Nm for 0.83m/s^2 acceleration
862.6rpm for 45kmph max speed

I'll show how I came to these numbers after I learn how to upload pics here. This is my first post here
 
Run time. 75minutes on a go kart track of 1. 2km. That's my first priority. Then is speed, above 40kmph.
 
The top speed will be limited by the input power and the aerodynamic drag. The Grin motor simulator will give you some idea what changing parameters does to performance:

http://www.ebikes.ca/tools/simulator.html

For sure avoid using lead-acid batteries. Lithium batteries of the same capacity will deliver about twice the run time and be 1/3 the weight.

I think the critical part will be motor choice and getting the gearing optimized. The rest is constrained by the rules. Better aerodynamics will be important too.
 
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