A particles lifetime in relation to the speed it travels with Is it possible for  a particles or any matter's lifetime in the universe to depend on it's speed?
 A: One thing that you have to remember is that the laws of physics are the same in all reference frames. 
Lets say there exists some particle $A$ which is stable for $t_o$ seconds when it is at rest. From its own reference frame, its lifetime HAS to be $t_o$ seconds regardless of the velocity with which it travels, because the laws of physics which apply to it are same whether it as at rest or travelling at 99% of the speed of light with respect to something. The amount time for which it remains stable when observed from its own reference frame is called the proper lifetime.
Its lifetime when observed by other observers is indeed speed dependent. If we observe $A$ when it is at rest, its lifetime would be $t_o$ seconds long. When $A$ moves with some velocity $v$ with respect to us, its lifetime would be: $$t'=\frac{t_o}{\sqrt{(1-(\frac{v}{c})^2)}}$$ This comes from special relativity. $c$ here is the speed of light. A well documented experiment which shows this is the measurement of muon flux at the surface of the Earth. Muons are subatomic particles, and are produced on Earth when cosmic rays hit the upper layers of our Atmosphere. You can check this link out for some information and numbers from the experiment: http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/muon.html
A: Just to complete Hritik Narayan's answer: the lifetime of an unstable particle is by definition the average time before it decays in its rest-frame. So whatever the frame used, the lifetime remains the same. Now, as already mentioned, what you measure experimentally does depend on the frame and thus on the velocity of the particle. You do have to correct for it (by making the appropriate boost) to deduce the lifetime (the number appearing in the particle data group for instance).
