For collisions wouldn't the distance traveled during the collision be the same? The energy lost is from heat, sound, deformation, etc. but wouldn't the work done on each car be the same since during the duration of contact they have to move the same distance (as soon as they move different distances they are no longer in contact) and apply the opposite but equal force? So is there a set ratio of kinetic energy lost for each object? If not, can anyone give me an example where the force is applied over different distances for a collision because I can't think of any examples.