NEET Physics Motion in a Straight Line / सरल रेखा में गति NEET PYQ-One Dimensional Motion

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 [NEET 2015 (C)]

A) \[-2n{{\beta }^{2}}\,{{x}^{-2n-1}}\]

B) \[-2n{{\beta }^{2}}\,{{x}^{-4n-1}}\]

C) \[-2{{\beta }^{2}}\,\,{{x}^{-2n+1}}\]

D) \[-2n{{\beta }^{2}}\,\,\,{{e}^{-4n+1}}\]

Correct Answer: B

Solution :

Given, \[v=\beta {{x}^{-2n}}\]

\[a=\frac{dv}{dt}=\frac{dx}{dt}.\frac{dv}{dx}\]

\[\Rightarrow \] \[\,a=v\frac{dv}{dx}=(\beta {{x}^{-2n}})(-2n\beta {{x}^{-2n-1}})\]

\[\Rightarrow \] \[a=-2n{{\beta }^{2}}{{x}^{-4n}}^{-1}\]