For my Highschool physics class we are building battlebots using RC tank Gear Boxes(I have no idea about brand or anthing, they're black with a space for two electric motors held together by magnets to sync them, and some gears and axles) My teams plan calls for a bot that pushes other bots like a bulldozer and for this we need to optimize our torque and not our speed from our electric motors. How should I go about doing this? Any advice is welcomed.

Thank you
Himay

Ever check out Robot Magazine?

http://www.botmag.com/

Assuming your not allowed to modify the gearboxes or use different motors than the other teams. You could use the smallest drive wheel you can to increase torque. Double up on the wheels for more traction (like a dually pickup truck).

Another option is to drive a secondary reduction off your gearbox. I.e. put a small gear or sprocket on the gearbox output shaft which would be driving a larger gear or sprocket attached to your drive wheel.

Steve

Use neumatic tires with low pressure or rubber cleated tracks as the more ground contact you have the increased friction is available.

You could partially fill the neumatic tires with water like farm tractors do for better traction.

(I studied Physics as well)

As for motors and gearboxes, use the highest RPM motor you can find and overvolt it such that the maximum efficiency of the motor is say at half the RPM when it would presumably be under load pushing another bot around.

For the gearbox, make it bullet proof as all the load will be transfered to the gearbox.