What is the force that throws you back into your seat when the car races off the line? And what is the force that throws you forward when the car brakes suddenly? What is the force that pins you against the door when the car makes a sharp turn?
The answer to all the above? None. It is the lack of force that “throws” you around in the car.
Watch the video below. See whether you can explain the motion of the tissue box placed on top of the dashboard.
Sitting on top of the dashboard, the only horizontal force acting on the tissue box is friction.
At around 0:12, the car made an emergency brake and slowed down abruptly. The tissue box hardly slowed down since the frictional between the tissue box and the dashboard falls far short of the required retardation force. As the tissue box remained in motion while the car comes to a screeching stop, it appears to jump forward.
At around 0:15, the car was rammed from behind by another car and lunged forward. The tissue box (which had already come to rest a split second earlier, thanks to the retardation force provided by the implacable windshield) could not keep up with the car. As the tissue box remained at rest while the car lunged forward, it appears to jump backward.
So there is no “phantom” force. It is just the inertia of the tissue box.