Question

It is common to speak of momentum as a "quantity of motion". It is not clear to me how this can be, as motion is change in displacement and measured by d/t. Nor does m.v have such a dimensionality.

Answer 1

That's someone's slang - don't take it literally

Answer 2

Indeed, it is not to be taken literally. Colloquialisms and slang enter into scientific terms all the time, and we often use the wrong expressions for quantities in everyday life. When we buy food for example, it comes in quantities of 250 grams "weight" as opposed to 250 grams mass.