Solution to 1996 Problem 44

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.

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