Physics education research, electronic materials, and the musings of Christopher Moore, Ph.D.

This year for the science fair I would like to do an experiment involving time dilation.  My current hypothesis (although it is subject to change, I am sure) is: Does a radioactive isotope decay at a slower rate when in motion? 

I am aware this is an ambitious experiment; it goes along the lines of the muon experiment that proved time dilation.  So I have several questions, so I can determine whether this experiment is out of my league fthis year.

1.  Is it possible to buy radioactive material without a license of some sort?  (Michio Kaku got Sodium-22 somehow when he was in high school...)
2.  Obviously I need a way to accelerate these radioisotopes to high speeds (a pretty good fraction of the speed of light) for there to be any noticeable difference.  Is there any alternative way to do this to building a home-made accelerator?
3.  How would I measure the decay rate of the radioisotope?
4.  And last but not least, what is the equation for time dilation, and what does each variable represent?