A particle of unit mass undergoes one dimensional motion such that its velocity varies according to `v(x) = `= beta x ^(-2n)` where B and n are constants and x is the position of the particle. The acceleraion of the particle as a function of x, is given by :

Options

A. `-2n beta ^(2) n ^(- 4n-1)`
B. `- 2 beta ^(2) x^(-2 n+1)`
C. `-2n beta ^(2) e^(-4n +1)`
D. `-2n beta ^(2) x ^(-2n-1)`

Answer

A

Explanation

`v = beta x ^(-2n)`
`So (dv )/(dx) = - 2n beta x ^(-2n -1)`
Now `a = v (dv)/(dx) = (beta x ^(-2n)) (-2n beta x ^(-2n -1))`
`implies a =- 2 n beta ^(2) x ^(-n -1)`