How did all of the heavy elements on earth get here? I have often read that a first generation star went supernova and seeded our solar system.  It is well known that stars that go supernova are the source of elements heavier than iron. I guess I am having trouble with these statements for the following reasons: 


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*The ejected matter from supernovas must be moving at a good fraction of the speed of light. So if the ejected matter is moving this fast, how can it seed our solar system? Wouldn't the ejected matter have to be moving slow enough to attract gravitationally? (Maybe a better question is what does seeded mean in this case because I clearly do not understand.)

*What does a first generation star mean here? Is this a star that was formed earlier in the universe’s life or later on? The reason I ask this if the supernova occurred early on when the expansion of the universe was fast, then I could see how a supernova would seed a solar system.

 A: The ejecta of a supernova does indeed move at a fraction of the speed of light (somewhere around the 10% mark). However, it does not remain at this speed forever. As the supernova ejecta expands outwards, it creates a shell of material that is actually gathering up particles in the ambient medium (typical interstellar densities are around 1 particle per cubic-centimeter, much higher in molecular clouds).
After a few hundred years, the supernova remnant enters the Sedov phase in which the velocity of the ejecta moves at approximately
$$
v(t)=\beta\left(\frac{E_0}{n_0}\right)^{1/5}t^{-3/5}\,{\rm pc/s}
$$
After a few thousand years, the remnant's velocity slows down to approximately the speed of sound of the interstellar medium (a few km/s)--at this point we cannot distinguish the supernova remnant from the interstellar medium. The material that was part of the star is mixed in with the surrounding interstellar medium, thus seeding it with heavier elements.
As for first-generation stars, typically this means the metal-poor stars (where metal-poor typically means $[Fe/H]=\log_{10}(N_{Fe}/N_H)<-1$) that we call the population II stars, as opposed to the more metal-rich population I stars. Rarely does it mean the cosmologically-old population III stars (note that we have not actually observed these, so they're still hypothetical; James Webb Space Telescope might be able to catch the remnants of these) which have a metallicity of approximately zero (purely H & He).
A: When the universe formed, matter that existed coalesced into proton and neutrons and eventually into atoms. It has been described that the lightest elements formed first, mostly hydrogen, which further were transformed through Fusion in stars to heavier elements such as Helium and trace amounts of Lithium and Beryllium. It is known that average to smaller stars are fueled by Fusion from hydrogen to Helium, and similarly bigger stars fuse heavier elements to form even heavier elements. Instead of reasoning that the elements reached earth through an asteroid or supernova flare(s), it seems more probable that earth is a burnt out star, that has gone through all the phases of a star and therefore has ample amounts of elements of the heavier variety. 
