Physical Mass and Relational Speed are related only in a system where both are valid considerations. In the case of our tangible universe, one would be hard pressed to isolate one from the other making them always directly related to that of the observer. However, multiple answers exist depending upon various considerations and indirect viewpoints. Simple questions at times are the most complex. It has always been a challenge to see things outside of the box, truthfully. We can say, I believe with certainty, that the present connects us to the observable. So, does this always mean mass and relational speed correspond with inflation? Ponder on. Take, for example, any rest mass or inert substance under consideration, the penny in your hand for example. Location, location, location. This is what gives us one answer over another, the frame reference that we decide to use; here or there? There are so many considerations to your fundamental question that most if not all still scratch heads over the basic principles involving space, time, speed, energy, substance, parabolic or hyperbolic relations, etc.
My dear friend, books have been and are yet to be written concerning your simple inquiry. As for the penny, at rest mass for you, seemingly without velocity, is our illusion. My vague memory tells me that we propel about the Sun at some odd 65,000 miles per hour and in relation to the galactic core, perhaps 500,000 miles per hour. Still, these are yet relatively low speeds in relation to what the Red Shift indicates with a universal universe edge approaching the speed of light in all directions. So, if I looked back from that distant edge of our universe to the penny in your hand, its mass would appear unchanged, yet traveling at the fantastic speed of near light speed. You see how mass and speed need that third element of location to make precise judgments. I might add in fact, that a fundamental premise for the way absolute time works is that all mass falls forward at the speed of light causing all mass to be in a state of inflation which we do observe (If it were The Big Crunch, we would observe deflation which has not been observed). For the tangible, all things are in motion. Time stops for no man. It is in different relative present speeds, in space, that calculates various openings out, or in, perspective wise. My high school teacher once told me that if mass opened to the speed of light, that it would timelessly and instantly expand to the size of the universe. Seeds from the past. This link may help you - http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/tdil.html . Good luck in your continued thinking!