Q. Why should Jews not drive on Shabbat?
The Torah commands us to rest and not to work on Shabbat, commemorating that G‑d created the world in six days and rested on the seventh. However, the Torah does not define what 'rest' and 'work' is. According to Jewish tradition there are 39 types of actions that are forbidden on Shabbat. Those 39 actions were all found in the building of the Mishkan - the movable Temple that moved around with the Jewish people while they were in the desert.
One if the 39 actions prohibited on Shabbat is lighting a fire. Causing a fire to be lit would be part of this prohibition. When driving a car, the internal combustion engine burns gas as you drive, making driving an activity that is forbidden on Shabbat.
Taking a ride when someone else is driving or riding a bus would also be forbidden. When a car or bus has more weight in it, the engine must burn more fuel to travel the same distance. By ridding in a car you are indirectly causing the car to burn more fuel, lighting more fire.
It might seem that limiting what we can do on Shabbat takes away from our Oneg – pleasure on Shabbat. However, the rest of Shabbat is not just a day of physical pleasure but of a unique spiritual experience that can only be felt without doing all of our usual activities.