What happens to the molecules average velocity?
So, there are two potential answers to this question, because I don't know how precisely the question was written. Part 1 will be if I take this question EXACTLY as it's written, and part 2 will be the answer to this question the way I assume the question was MEANT to be answered.
In a gas, you have a distribution of speeds known as the Maxwell-Boltzmann distribution. There is an average speed of the gas that is nonzero, and you can find it using the distribution.
HOWEVER, all directions of motion for the gas are equally likely, so even though there is a non-zero average speed, the average velocity WILL be zero.
So, changing the temperature of the gas has no affect on the average velocity, which will always be zero.
Now, what I think this problem meant for you to do is to relate the average speed of the gas to the temperature. This is not zero, as I mentioned above. The equation relating the two is:
v_av = SQRT(8RT/piM)
where R is the ideal gas constant, T is the temperature of the gas, and M is the molar mass of the gas.
In this case, it's clear that if T becomes 2T, then vav becomes SQRT(2)*vav, since the average speed is proportional to the square-root of the temperature.
If this problem was written by your professor, I would ask him/her what they meant in the problem. If this is for an online homework system like Mastering Physics, I would go with the literal answer, part 1. If that's wrong, then put in the answer for part B.