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# The position $x$ of a particle at time $t$ is given by $x=\large\frac{v_0}{a} $$(1-e^{-at}) where v_0 is constant and a >0 find the dimensions of v_0 and a $(a)\;M^0LT^{-1}\;and\;T^{-1} \quad (b)\;M^0LT^0\;and \;T^{-1}\quad (c)\;M^0LT^{-1}\;and\;LT^{-2} \quad (d)\;M^0LT^{-1}\;and\;T$ Can you answer this question? ## 1 Answer 0 votes a \times t is dimensionless quantity a=\large\frac{1}{t}$$=[T^{-1}]$
also $x=\large\frac{v_0}{a}$ and $v_0=x \;a$
$v_0=LT^{-1}$
$\quad=[M^0LT^{-1}]$
Hence the dimensions of $v_0=M^0LT^{-1}\;and\; a=\;T^{-1}$
Hence a is the correct answer.
answered Jun 17, 2013 by
edited May 29, 2014

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