thread closed, thanks
If it doesn't shoot far enough with the existing supply, I can't really see powering it via PWM is going to improve range.
I have been assigned the task
Is this your homework that you should be doing yourself?
AWOL:
If it doesn't shoot far enough with the existing supply, I can't really see powering it via PWM is going to improve range.
Would it decrease range by alot? or just keep it the same?
Is this your homework that you should be doing yourself?
It is a group project, and they never said we couldn't ask for help outside of class.. So I am just trying to find what the best path would be for us to take 
Would it decrease range by alot?
It will decrease it certainty because the motor would not be on all the time and so would not go as fast.
and you can only use 2 AAA batteries (3V).
You would need to power the arduino with that?
If so then it would be even slower because you would have to switch it with a transistor and you would get a voltage drop with that.
Are you allowed to use a booster circuit, that is a switching regulator that gives you more voltage to drive the motor. Something like a minty booster.
You would need to power the arduino with that?
Yes, so your saying use a booster to up the voltage of the batteries so that they can run the arduino and motor at max speed? Are there any easy circuits available for this?
If all you need is to boost the motor voltage, what does the Arduino gain you?
Are there any easy circuits available for this?
Yes
http://www.ladyada.net/make/mintyboost/
what does the Arduino gain you?
You and I both know it is nothing, but it looks like he needs to learn by seeing for himself.