First of all, I am going to assume that instead of emerging from the tunnel in the beginning, I am going to say that the two cars are entering the tunnel. They cannot leave the tunnel twiceso I am guessing that that was a typo.

if car B spends a minute in the tunnel then it will have accelerated to 100km/h. And if car B spends a minute int he tunnel then it will also have accelerated to 100km/h. Therfore I think that if the cars spend less than a minute int he tunnel than car A will come out first because car B hasn't had enough time to accelerate up to A. However, if over 1 minute passes than car B will come out first because it accelerates faster.

Neither car would pass each other. This is due to the fact, that although car B has a slower speed it has enough acceleration to make up for the difference in distance that would occur between the two cars. I think that Car B would pass Car A because it has a higher acceleration. I know that Car B is going slower, but it just seems that would be logical that with a faster acceleration it would eventually pass Car A.

From the given information, I believe it is hard to determine which car will emerge first. Car A has a higer velocity then car B but car B has a higher acceleration then car A. IF they emerge from the tunnel side by side, car A would be ahead since it has the higer velocity, but over a brief distance car B would pass car A because it has a higher acceleration. The length of the tunnel might also aid in drawing this conclusion.