Cozmo
You may have already done this, but how about going and putting a few posters up near to where you hit the cat, it could just say "Longhaired ginger cat - is this your cat or have you seen it since (whatever time accident was) on 22nd April? Please call (then put your phone number)" - that way if it has made its way home or to a nearby house/garden/driveway you will at least know if it is home/safe/injured/taken to a vet.
I had a very close call with a cat at the other end of my road a couple of years ago, it ran diagonally across the road in front of me (so it was going the same direction as me) - to this day I have no idea how I didn't hit it. Same with a rabbit yesterday, it ran right under my car but got away somehow!
My own (currently missing) cat Bazza chased another cat out of our garden once and unfortunately it ran straight into the side of a car. The cat did survive and the driver took it to a nearby vet, and the whole experience taught Bazza to stay out of the roads and away from cars, but not all cats understand unfortunately.
I should add that we live in a quiet residential road, not a particularly busy route - but these kind of accidents really can happen anywhere.
If the cat was able to get off the road hopefully it has been found by someone by now and is being checked over by a vet right now