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If you use a standard DC gearmotor of the type shown you will need to attach a sensor of some sort to the output shaft so that the rotation speed can be determined. The Arduino, when suitably programmed, can respond to the sensed speed and adjust a PWM (pulse width modulated) drive to the motor to maintain a given speed.
The motor will also need a reverse-biased diode connected across its terminals to suppress high voltage spikes which can destroy the driver transistor. I note that no such diode is apparent in the video !!