We will from first principles examine what adding acceleration does, and will not do as to the HUP previously derived. In doing so we will be examining a Friedmann equation for the evolution of the scale factor, using explicitly two cases, one case being when the acceleration of expansion of the scale factor is kept in, another when it is out, and the intermediate cases of when the acceleration factor, and the scale factor is important but not dominant. In doing so we will be tying it in our discussion with the earlier work done on the HUP. The ratio of 2nd derivative of a (time derivative), divided by a (a is a scale factor) set equal to zero would mean that the ratio of the 1st derivative of a (time derivative) divided by a could have complex solution roots, whereas the ration of the 2nd derivative of a (time derivative) divided by a with a, the scale factor as a ration not equal to zero, but constant, and large would frequently imply the first time derivative of a divided by a would have three dissimilar real valued roots. From the sake of physical analysis, the situation with not equal to zero yields more tractable result for which will have implications for the HUP inequality