Based on your description of the protist having long lash-like appendages, it is likely that those appendages are flagella. In many protists, flagella move in a whip-like or undulating manner, propelling the organism forward.
The most accurate response would be: The appendages of this protist will move back and forth like a wagging tail to actively propel the protist forward.
This describes the typical movement of flagella, which are used for locomotion in various protists.