RIGHTARROW V_x = \frac{{dx}}{{dt}} = {u_0}\left( {1 + \frac{{3x}}{L}} \right)\)SEPARATION of variable\(\Rightarrow \frac{{dx}}{{{u_0}\left( {1 + \frac{{3x}}{L}} \right)}} = dt\)Integrating the equation form 0 to T (Required TIME)\(\mathop \smallint \limits_0^T dt = \mathop \smallint \limits_0^L \frac{{dx}}{{{u_0}\left( {1 + \frac{{3x}}{L}} \right)}} = \frac{1}{{{u_0}}}\frac{L}{3} \cdot \left[ {\ln \left( {1 + \frac{{3x}}{L}} \right)} \right]_0^L\)\(T = \frac{1}{{{u_0}}}\left[ {\ln \left( {1 + \frac{{3x}}{L}} \right)} \right]_0^L \cdot \left( {\frac{L}{3}} \right)\)\(= \frac{L}{{3{u_0}}}{\rm{ln}}\left[ {1 + 3} \right]\)\(T = \frac{L}{{3{u_0}}}\ln \left[ 4 \right]\)