# 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 ?

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

Let the time taken to cover the first half portion of the journey be $t_1$ and for the second half portion be $t_2$ . Then
$t=t_1+t_2$
For the first half-journey, putting
$S= L/2,u=0$ etc. in $S= ut+ \large\frac{1}{2} $$at^2, we get \large\frac{L}{2}$$=0+\frac{1}{2} $$at_1^2 \large\frac{L}{2}$$=0+ \large\frac{1}{2}$$at_1^2 As the time to complete the whole journey is t, therefore , L= 0+ \frac{1}{2}$$at^2$
Dividing both equations :
$L= 0+ \large\frac{1}{2}$$=> t_1 =\large\frac{t}{\sqrt{2}}$
$t_2= (t-t_1)=t- \frac{t}{\sqrt 2}=t \bigg[\large\frac{\sqrt 2-1}{\sqrt 2}\bigg]$
Hence A is the correct answer.