A block of mass \( 1 \, \text{kg} \), moving along \( x \) with speed \( v_i = 10 \, \text{m/s} \) enters a rough region ranging from \( x = 0.1 \, \text{m} \) to \( x = 1.9 \, \text{m} \). The retarding force acting on the block in this range is \( F_r = -k x \, \text{N} \) with \( k = 10 \, \text{N/m} \). Then the final speed of the block as it crosses rough region is:
