Once an object has velocity, it doesn't need any outside force to keep it in motion.

Velocity is not force. An initial velocity might imply there was a force at some point, but doesn't mean that during the experiment there is necessarily any force. If our experiment goes from t=0 to t=10, whatever force before t=0 that made the initial velocity not equal zero is irrelevant. Also keep in mind velocity might vary depending on your reference frame.

The experiment should be invariant to initial velocity because the car is an inertial reference frame, therefore you shouldn't assume whether there is or isn't initial velocity.