Fasting means RESTING. You shouldn't be doing anything other than staying in bed while fasting. You are defeating your purpose.
While fasting, you can get light-headed and you do not want this to happen while driving.
Expending any energy doing anykind of mental activity (driving requires focus and concentration) or physical activity is not letting that energy go towards healing and rejuventation. This is not the way to fast, in my opinion.