Motion is said to be happening when any object moves and sound is produced by vibration. Vibration also happens when something moves. So, yes, motion produces sound by vibration.
For example when you it a stone with a wall, you hear a sound. in this case during collision motion of stone and a vibration takes place which results in sound. another example; when you speaks a vibration occurs in you throat, your vocal cords vibrate. The vibration of the vocal cords produces a sound.