I'm not sure what the author's target audience is, but:

> But we know from high school physics that a = v' = p''

It would be exceedingly rare to see "p" used as the position variable in high school physics - it's almost exclusively reserved for momentum.

Most high school students do 1D physics with position as "x". Those who go on to study more physics usually use "s" as their displacement function/vector and maybe "r" as a position vector.

(Also, the overwhelming majority of high school physics students never touch calculus-based physics -- only about 50-60 thousand students take the AP Physics C exam each year. 5 times that take AP Physics 1, and even more take non-AP Physics.)