The image above is one of a series that I call Just Passing By. I have added a few more examples to my "Abstracts" gallery, so please visit that gallery as well as others on my website where I have added a few more images.
This series was made from the car. I was not driving and would not attempt to do this kind of photography unless someone else is at the wheel. From the passenger's seat I look ahead for possible subjects that I feel would look good "in motion". To achieve this effect, I use a slow shutter speed. Try a few exposures at different shutter speeds as you ride along to find what looks best to you. I have used exposures between a quarter of a second and one second. Sometimes the flow of traffic will determine what shutter speed you might like to use. Slower traffic might equal longer shutter speeds and faster traffic might equal shorter shutter speeds. That, obviously, is just a rule of thumb. (But wait, there are no rules in photography!) It's all a matter of chance and you may, or may not, get something you like.
I suppose you and your driver could circle around and try again if you don't get exactly what you want, but I prefer to hope for the best and take what I get. I also like to have subjects that are recognizable in the photograph. Using exposures that are too long obscures the subject and produces just a blur of color (there is nothing wrong with this if that is what you want). You may get some wonderful background layers that you can use with other images.
I look for subjects that are relatively close to the road as they will exhibit the most amount of motion and distortion. Far away subjects will not show as much motion and distortion unless you use a longer exposure or a longer lens. Give it a try. It is all an experiment, the results are limitless, and you can get some wonderful one of a kind photographs.
If you would like to try this kind of photography, please keep in mind your safety, the safety of others, and DON'T TRY THIS WHILE DRIVING!