Last thing. What is this, and should any hose bee attached to the front of it as well

[Mäwby]

Help? My scooter keeps cutting off after riding for a bit, and I wonder if this could be the culprit. The battery will die also and I can't even start it. I never fully charged the battery when I first got the scooter. I charged it full last night, and will give it another go today to see if that may have been the issue.

Please chime in.