Arduino Uno General Power Distribution Question

Other Hardware General Electronics
1

My set up is an Arduino Uno w/ R3 Motor Shield connected to an HC-SR04 ultrasonic sensor and two high speed RC helicopter motors. My project is for a competition where the power source is limited to a 9V battery and 4 AA batteries.
My initial setup was connecting the 9V to the boards power adapter and the 4 AA batteries to the Vin and GND connection on the motor shield.

I want to increase the speed of my car so my question is, is it safe for the board and more beneficial for increasing the motor speed if I connect the 9V to the Vin and GND connection and the 4 AA's to the power adapter?
Or is it the same either way? My team's consensus was that connecting the 9V to the Vin and GND connections would provide more direct power to the motors but i am not familiar with the boards power distribution which is why i posted is question (obviously).

Any help preventing me from damaging the board or wasting my time would be very appreciated.

2

basically you can make any voltage from 9V. You can even go higher if needed. For the Arduino you only need 5V so use a buck converter to go down to 5V and a boost from the battery if a higher voltage is needed. Putting 9V on the arduino is wasting (9-5) * current used by Arduino milliwatts of energy.

3

Small 9V battery can barely power an Arduino, let alone motors - it doesn't have
anything like the current rating needed. So Vin for that (Vin can be 7V to 12V).

Motors need high current supply (if the current sourcing isn't up to what the motors
need the voltage is immaterial).