Hmm. Think of the response that acceleration would have, all else equal, if momentum increased.
There's two ways to change momentum -- velocity or mass. If mass increases, acceleration decreases. If velocity increases, acceleration remains the same.
Edit: You've got a bit of an endogeneity problem in your equation. And I guess I do, too.
momentum = 1/2 * mass * acceleration * time ^ 2
Since momentum is equivalent to mass times velocity, one of its components is on both sides of the equation simultaneously. My original equation had the same problem, except with velocity instead of mass.
So... I think "momentum" here is leading us a bit in the wrong direction. What the author should have been saying is "mass". After all, the metaphor was "a heavy ball", emphasizing the weight. The initial velocity was unchanged across the comparison.
It bugs me that so many domains misuse the term "momentum". Business people confuse momentum for velocity. Now machine learning folks are confusing momentum for mass. It's common for people to use a component of the whole as a stand-in term, like "my wheels" instead of "my car". Less common to go the other way: "my arm hurts" instead of "my elbow hurts". In this machine learning case the imprecision of the metaphor harms understanding.
