You take a 3 kg metal block and slide it along the floor, where the coefficient of friction is only 0.4. You release the block with an initial velocity of $\langle 6, 0, 0\rangle m/s$. How long will it take for the block to come to a stop? How far does the block move?

$ x: \Delta p_x = -F_N\Delta t $

$ y: \Delta p_y = (F_N - mg)\Delta t = 0 $

Combining these two equations and writing $ p_x = mv_x $, we have

$ \Delta(mv_x) = -mg\Delta t $

$ \Delta(v_x) = - g\Delta t $

$ \Delta(t) = \dfrac{0 - v_{xi}}\{-g} = \dfrac{v_{xi}}\{g} $