newxalbertus Or should we be moving the character only with the animation movement and check the character position over time?
Yes, the concept of root motion is to let an animation dictate movement of the character, moving it's main GameObject including any physics components.
You would either modify the playback speed of the animation, have different animations for fixed speeds (like e.g. walk and run) or have an interpolation between walking and running (a mix of the two animations) to get any speed in-between walk and run speeds.
BTW: If your character slides during a walk animation, you don't necessarily have to use root motion but could instead calculate the distance per walk-cycle and adjust either the animation speed to desired movement, or adjust the movement distance to the animation. Games have been doing that for decades.