Because F=ma, all forces are unstoppable except where the mass of the object it impacts is infinite, at which point you have an object which cannot be affected in any real sense by a force. As such, the chances are that if an unstoppable (i.e. normally finite) force meets an immovable object (i.e. infinite mass), the object will be stationary.
However, the logical way to deal with this is to state that in any coupled situation, the existence of an unstoppable force and an immovable object are contradictory and one must take priority over the other.
Travel at light speed for a car would be impossible. However, assuming 99.999% of the speed of light, if you turned on your headlights you would see the light extending ahead of you at the speed of light from your frame of reference. One of the joys of relativity is that light speed is constant in all frames of reference, moving or otherwise.
An observer will see a totally different story, however.