Arduino powered with a 12V car battery ?

I can't make sense of your diagram (also, please reduce images to 640x480 so we can view them easier).

You have a single cell battery in the image, or is that meant to be the 12v battery?

You have a rectangle with 2 + connections and 2 - connections - what is it?

You seem to have the motor permanently connected to the battery and you seem to have a transistor that will short-circuit the battery.

I don't see any sign of an Arduino.

But it wouldn't surprise me to find I am wrong.

...R