The coefficient of restitution is . You just got your new car. You want to experience it. You floor the gas pedal, and you experience a force pressing you back into your seat. This force is a fictitious force.
Fictitious forces appear in accelerating reference frames .
Such frames are not inertial reference frames. The accelerating reference frame in the above example is accelerating with your car. In this frame your car is at rest. You are at rest in the car, but a force is pushing you against the back of your seat. To your friend observing you from the sidewalk things look different.