The math for recharge rate is easy, it holds 50 kwh. The voltage would get fairly low as the cap discharges so you probably would not be using the bottom 5 kwh if you could help it. So basically you would need to figure out how fast you can move 45 kwh.
The other question is can you really drive 500 miles on 45 kwh.
As I have mentioned before, an electric car is going to be significantly easier to push down the road than a gasoline car.
The other factor is speed. Air drag goes up by the cube of speed. Using your math, a car that gets 40mpg at 60 mph should be using about 6 hp at 50 mph. That matches my memory close enough.
A gasoline car has to be engineered for economy at different speeds. Electric motors also vary in efficiency based on rpm but vary much less than gasoline engines. They remain efficient at low rpm whereas gasoline engines are not very efficient at low rpm. The electric car will probably get a very large number of miles per kwh when tooling around town but people will get a suprise when they get on the highway and set the cruise at 80 mph. It takes a fraction of a horsepower to go 10 mph but probably takes about 50 hp to go 80 mph.
One question, a BTU is a unit of energy, hp is a measure of power, it’s been too many years since school, BTU equals hp over what time period?
It is not 50kwh.
At 15kw to go 60 mph.
To go 500miles at 60 mph it will take 8.3 hrs
8.3 times 15kw is 124.5 kwh.
Batteries discharge exponentially faster as load increases. So you might be able 500 miles at 30 mph using 50kwh but I seroisly doubt you will get anywhere near that at highway speed.
None the less, 45kwh in five minutes is still 900A at 600VDC. Which would mean 4 ea 500kcmil cables. I doubt many people would be able to lift the plug off the ground.
This recharge is not for the faint of heart.
Essentially this storage system is a super capacitor, which is fine by itself, but what happens in an accident and it shorts out? It will be a industrial size plasma cutter.