rate of speed

A rate is a ratio of two linearly related quantities, or more generally, of the variations of two functionally related quantities. A rate of exchange, for example, is a ratio of equivalent amounts of two types of currency, and a birth rate is a ratio of the number of births per unit time to the size of a population.

Time is often understood to be the independent variable involved in a rate, which is then the ratio of the number of occurrences of an event, as a heart rate, or the change in some quantity, to elapsed time. Thus, the speed of a moving object is the rate of change of its displacement. If the term rate of speed is to be assigned any meaning at all, it can only be as an elliptical variant of rate of change of speed, i.e., a circumlocution for acceleration. When the phrase appears, however, it is always just a bloated barbarism for speed.