The acceleration is the time derivative of the velocity. We use the chain rule to obtain:

$\begin{align*}a = \dot{v} = \beta (-n) x^{-n-1} \dot{x}\end{align*}$

But $\dot{x} = v = \beta x^{-n}$ , so

$\begin{align*}a = \beta (-n) x^{-n-1} \beta x^{-n} = - \beta^2 n x^{-2 n -1}\end{align*}$

Thus, answer (A) is correct.

Solution to 1996 Problem 44