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NEET 2015
Exam
NEET
Year
2015
Subject
Physics
Chapter
Motion in One Dimension

NEET 2015 · Physics · Motion in One Dimension

A particle undergoes a one-dimensional motion such that its...

A particle undergoes a one-dimensional motion such that its velocity varies according to v(x)=\betax−2nv\left(x\right) = \betax^{- 2n}, where β\beta and n\text{n}~are constants and xx is the position of the particle. The acceleration of the particle as a function of~xx& is given by

Options

  1. A−2nβ2x−2n−1- 2n{\beta}^{2}{x}^{- 2n - 1}
  2. B−2nβ2x−4n−1- 2n{\beta}^{2}{x}^{- 4n - 1}
  3. C−2nβ2x−2n+1- 2n{\beta}^{2}{x}^{- 2n + 1}
  4. D−2nβ2x−4n+1- 2n{\beta}^{2}{x}^{- 4n + 1}

Correct answer

B. −2nβ2x−4n−1- 2n{\beta}^{2}{x}^{- 4n - 1}

Step-by-step solution

According to the question

a=vdvdx=v(ddxβx−2n)a = v\dfrac{dv}{dx} = v\left(\dfrac{d}{dx}\beta{x}^{-2n}\right)

=(−2nβx−2n−1)βx−2n= \left(- 2n\beta{x}^{-2n - 1}\right)\beta{x}^{- 2n}

=−2nβ2x−4n−1= - 2n{\beta}^{2}{x}^{- 4n - 1}
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