What Martin said. The only thing I would change on the modifier is check fixed position. The offset will now be 0 to 1 with 0 being start of curve and 1 being end of curve. Then you can keyframe the offset or use a drive pointing to a bones location. The you can just move the bone 1 meter to move it to the end of the curve.
The skill to do the driver method is covered in the shapes course.
