The accelerating expanding universe

You are on the right track actually, let me make a few corrections off the top of my head:You are right in saying that the acceleration has been taking place for billions of years, but your rate of increase is probably off. The interesting thing is that the more distant a galaxy, not only the faster it appears to be receding, but also it appears to be increasing in that speed faster than closer galaxies. In other words, the speed at which a galaxy recedes from us appears to be proportional to the amount of space between us and the galaxy.My point is that a constant rate of increase is not fully accurate, so if we observe 1 mph/y now, that wasn't always the case. Also, it is certainly possible to measure small rates of acceleration of such distant objects.

Err, no.Hubble's law is the observation that galaxies are receding from us at a speed proportional to their distance from us. Hubble's constant is the constant of that proportionality, usually stated in (km/s)/Mpc which is kilometers per second for a galaxy one Megaparsec away.So, what this means is that a galaxy one Megaparsec away is receding at a particular speed, and one two Megaparsecs away would be receding at twice that speed. Since the more distant galaxies have a higher velocity they are increasing in distance faster than slower, closer galaxies; ergo, more distant galaxies appear to accelerate away faster than closer galaxies.If they go faster with more space between us, getting more space between us faster means they go faster... faster. Even though Hubble's constant is constant.