Cosmic Rays in general are believed to be created from supernova explosions in our galaxy and possibly from other galaxies. Protons are ejected from the explosion at extremely high velocities, although this doesnt completely explain where the extremely high energy comsmic rays (10^20 eV) come...
for particles with a non-zero rest mass...
m = \frac{m_0}{\sqrt{1 - \frac{v^2/c^2}}}
This equation gives you the mass of a particle relative to you, going at velocity v.
particles with a zero rest mass, for example, photons, naturaly travel at the speed of light, they cannot travel slower...
start off with the definition of acceleration...
a = \frac{v_f-v_0}{t}
v_f = v_0 + at
Definition of average velocity...
v_{ave} = d/t
d = \frac{v_f + v_0}{2}t
substitute...
d = \frac{(v_0+at) + v_0}{2}t
d = \frac{2v_0 + at}{2}t
d = v_0t + \frac{1}{2}at^2
For the second...
By saying "fast enough" im guessing you mean faster than the speed of light, which we all know is impossible. So from your example it would be impossible to time travel into the past, but it would be possible to time travel into the future because of time dilation.
As for time travel to the...
This is impossible, the mass of the proton is 1.67262158 × 10-27 kilograms, while the mass of the electron is 9.10938188 × 10-31 kilograms. This means that the proton has a mass more than 10^4 times that of the electron.
1) The direction of the atoms are completely random according to the Kinetic Molecular Theory.
2) Only the atoms move, the protons and neutrons are fixed in the atom as being the nucleus with electrons "rotating" around the nucleus. If the atoms move fast enough, some atoms will get ionized...
Neutrinos are definitly not massless, they have a rest mass. Particles with no rest mass, for example photons, DO have energy, which can be calculated by using the equation...
E = h \nu Where E is the energy, h is plank's canstant and \nu is frequency of the light.
I dont know much about black holes, but that equation you gave can be determined by knowing the mass of the black hole, since G and c are both constants. That bothers me a little, that you can calculate length from mass.