Question

A particle of unit mass undergoes one-dimensional motion such that its velocity varies according to $v\left(x\right)=\beta x^{-2n}$, 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. $-2{\beta }^2{x}^{-2n+1}$
• B. $-2n{\beta }^2{e}^{-4n+1}$
• C. $-2n{\beta }^2{x}^{-2n-1}$
• D. $-2n{\beta }^2{x}^{-4n-1}$

Answer 1

The correct option is D $-2n{\beta }^2{x}^{-4n-1}$

$v\left(x\right)=\beta x^{-2n}$

$a\left(x\right)=v\frac{dv}{dx}=\beta x^{-2n}\frac{d\beta x^{-2n}}{dx}$

$a\left(x\right)=\beta x^{-2n}{x}^{-2n}\times \beta (-2n)x^{-2n-1}$

$a\left(x\right)=-2n{\beta }^2{x}^{-4n-1}$