## IM Commentary

The purpose of this task is to provide students practice in drawing conclusions about expressions they might encounter in classes outside mathematics, by parsing them in terms of their algebraic structure. Teachers might stress the subtle difference between "seeing" why the expression must be zero and the more mechanical process of algebraically simplifying the expression upon substituting $v=c$. Although part (b) might initially be though of as an optimization problem in a calculus course, some elementary reasoning with the structure of the expression gives the same answer in a more fluid and conceptual fashion.

For reference, this formula is for the length contraction of an object travelling near the speed of light, denoted $c$. While the constant $c$ in the problem is indeed a positive constant, its positivity is irrelevant to the task at hand since only its square, $c^2$, appears in the formula.