Had that problem living in Michigan, where we had several close calls with tornadoes each Summer. Was living in a house on a slab foundation with no basement. Once I packed the family in a Ford Escort and outran it (would not recommend that).
If you dig down 4 feet or so you are likely to hit water here, which is why there are no basements. No, I wouldn’t recommend trying to out run a tornado. It’s not that they are moving fast, but rather because they can change directions very quickly. The other problem is getting stuck in a traffic jam situation. When there is absolutely no place to go and it is getting close, find the lowest level ground like a drainage ditch. Never get under an overpass either.