The reason the van stops and the dog keeps going is because the force that is stopping the van isn't interacting with the dog
Newton's second Law
The smaller car has gone farther because it has a smaller mass than the big truck, Newton's second law proves this is right because the larger the mass of an object the slower it will go and less distance it will travel when an equal force is applied to both cars.
Newton's third Law
Newton's second law explains how for every action there's an equal or opposite reaction. that's why when both cars are moved with the same force they go the same distance because they have the same mass