My back-of-the-envelope calculation, if covering an entire car with solar panels... Assumptions: car width is 5 ft, hood is 5 ft, roof is 3 ft, and trunk is 4 ft makes 60 square feet for the whole car. (Note, this isn't the dimensions from a Tesla, but from the older cars that I remember). High output solar panels are 15 watts per sq ft. So 900 watts output max (lets round it off to 1 kilowatt to make the math easy).

Now taking the rated specs from a Model S, a 60 kWh battery gets you 200 miles. So .3 kWh per mile. Therefore, leaving you car to recharge in the sun for 8 hours while you are at work, will get you home if you live within 25 miles. Assuming maximum efficiency of course. Note, that you can't put 60 sq feet of solar panels on the Model S, due to the long slope of the front and back windows, and redesigning it so that it has the non-window surface areas of my old 85 Chevy would make it less aerodynamic. But this gives you a good upper bound if I did my math right.

There just isn't enough surface area. A Model S has a roof area of around 9m^2. The sun provides about 1000W/m^2 on a clear day at high noon when directly overhead, so with 100% efficient solar cells on a perfect day, you'd get around 9kW of electricity. A Model S goes about 4 miles per kWh when it's doing well, so in this ideal situation you'd top out at around 36MPH. In the real world, the sun isn't directly overhead, and real solar cells have more like 20% efficiency, so cut that number down by a factor of ten or more.

The best way to build a solar-powered car would be to have a battery-powered car that gets recharged from solar energy. Basically, a Model S and a home solar generating system.

Unfortunately that was only science fiction. I don't think the sunlight that lands on a car would be sufficient by itself to charge the system to any acceptable level.