Yes you can do it. Easiest way is to start with a car that the engine does not run and transplant an electric motor in place of the engine. An electric vehicles website should shed some more light on the subject.
You can build you own electric car. Do some research online and read books about how to build your own electric car. There may also be some companies making kits.
Due to the hike in on going oil price most of the people around the world is now been thinking about powered motor car. Dry battery can substitute the power