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A particle of unit mass undergoes one-dimensional motion such that its velocity varies according to $v(x) = \beta x^{-2n}$, where $\beta$ and n are constants and x is the position of the particle. The acceleration of the particle as a function of x is given by
A
$-2n\beta^2 x^{-2n-1}$
B
$-2n\beta^2 x^{-4n-1}$
C
$-2\beta^2 x^{-2n+1}$
D
$-2n\beta^2 e^{-4n+1}$
Detailed Solution
$a = v\frac{dv}{dx}$
$a = \beta x^{-2n}\cdot \beta(-2n)x^{-2n-1}$
$a = -2n\beta^2 x^{-4n-1}$
$a = \beta x^{-2n}\cdot \beta(-2n)x^{-2n-1}$
$a = -2n\beta^2 x^{-4n-1}$