A rat is running on ice with speed $v=\pi \mathrm{m} {\mathrm{s}}^{-1}$. Suddenly he decides to turn by $90°$ and want to keep running with the same speed throughout. What is the least amount of time (in seconds) he needs for such a turn? Suppose that rat’s feet can move independently. Coefficient of friction between rat’s feet and ice is $0.125$. (Given: ${\pi }^2=g$ )