I've heard that when an object is accelerated at huge huge speeds they actually gain mass. Is there a formula to see how much mass an object would gain will going a certain velocity.
The problem you will continue to have with ones like this, is thinking of mass as actually changing with speed. That is a very old idea to think of the mass “as if it increases” with speed. Which works ok in a limited way, such as getting to E=mc^2. But modern science accepts the idea is incorrect in application and mass should be understood as intrinsic and unchanging with speed. Only momentum “p” or ‘mv’ is factored to increase with speed, and not mass.
The important concept to note here is that it is the momentum which increases, not the 'mass'. In my opinion, in special relativity only invariant mass should be considered and the whole notion of 'relativistic' mass should be abandoned in special relativity (the situation in general relativity is somewhat more complex). As Randall says above, the notion that mass increases is usually introduced when explaining the 'basics' of relativity in a general context, but leads to misunderstandings when it comes to formally learning relativity. Below are some links which you may wish to peruse;But for any real mass, while it remains the same at mo; as the speed increases it must create a momentum "mv" that if factored by relativistic "gamma" to a larger number than expected by classical thinking.
Thus momentum as v approaches c would approach infinity and creating it would require an impossible amount of energy to reach it.
so that's why, in my post, https://www.physicsforums.com/showthread.php?t=149350"[itex]E = mc^2[/itex] gives the energy equivalence of the invarient mass.