question_answer

The position x of a particle at time  by \[x=\frac{{{v}_{0}}}{a}(1-{{e}^{-a\,\,t}})\]where \[{{v}_{0}}\] is constant and \[a>0.\] The dimensional formula of \[{{v}_{0}}\]and a are

A) \[\left[ {{M}^{0}}L{}^{1}{{T}^{-1}} \right]and\left[ {{M}^{0}}L{}^{0}{{T}^{-1}} \right]\]

B) \[\left[ {{M}^{0}}L{}^{1}{{T}^{0}} \right]and\left[ {{M}^{0}}L{}^{0}{{T}^{-1}} \right]\]

C) \[\left[ {{M}^{0}}L{{T}^{-1}} \right]and\left[ {{M}^{0}}L{}^{1}{{T}^{-2}} \right]\]

D) \[\left[ {{M}^{0}}L{}^{1}{{T}^{-1}} \right]and\left[ {{M}^{0}}L{}^{0}{{T}^{1}} \right]\]