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Straight from rest and moving with a constant acceleration , a body covers certains distance L in time t. What is the time taken by the body to cover the second half portion of this journey ?

$\begin{array}{1 1}(A)\;t \bigg(\frac{\sqrt 2 -1}{\sqrt 2}\bigg)\\(B)\;t^2 \bigg(\frac{\sqrt 2 -1}{\sqrt 2}\bigg) \\(C)\;t^3 \bigg(\frac{\sqrt 2 +1}{\sqrt 2}\bigg) \\(D)\;t \bigg(\frac{\sqrt 2 +1}{\sqrt 2}\bigg)\end{array} $

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