The solar powered car has been one of the "holy grail's" of the auto industry for a long time. While it has been done in specialty projects with custom built vehicles and huge budgets, the best average speeds are less than 40 mph in the middle of the summer and the vehicles are so light that they risk being flipped by passing trucks. The problem is that it takes a lot of area exposed to the sun to collect much solar energy. Car roofs just don't have much area to collect the sunlight.
Your idea of storing the solar energy is good and will certainly help, however, it is unlikely that you can get more than a couple of miles of range after parking a car with solar cells on top in the sun for a day.
They people who do run their cars off of solar energy (and there are a lot who do) generally put the solar cells on the roof of their house (where there is a lot of area exposed to the sun) and charge their electric cars from those. Actually, even better, what most do is to have their solar cells connected to the normal electrical grid so that they sell electricity back to the power company during the day. During the day, the solar cells are most effective since the sun is shining, the power company needs the extra electricity to handle daytime airconditioning, and electricity is most expensive. They charge their EV's from the electric grid during the night when the power company has excess electricity so the prices are low. It all works together quite nicely.