$A$ particle of mass $m$ is constrained to move on the $x$-axis. $A$ force $F$ acts on the particle. $F$ always points toward the position labeled $E$. For example,when the particle is to the left of $E$,$F$ points to the right. The magnitude of $F$ is constant except at point $E$ where it is zero. The system is horizontal. $F$ is the net force acting on the particle. The particle is displaced a distance $A$ towards the left from the equilibrium position $E$ and released from rest at $t=0$. Find the minimum time it will take to reach from $x=-A/2$ to $x=0$.

• A
  $\frac{3}{2} \sqrt{\frac{m A}{F}}(\sqrt{2}-1)$
• B
  $0$
• C
  $2 \sqrt{\frac{ m A }{ F }}(\sqrt{2}-1)$
• D
  $\sqrt{\frac{ m A }{ F }}(\sqrt{2}-1)$