Napiszmy równanie ruchu:
[tex]m\ddot{x}=-k\dot{x}^2\\\dot{x}=V_x\\m\dot{V}_x=-kV_x^2\\\frac{dV_x}{dt}=-\frac{k}{m}V_x^2\\\frac{dV_x}{V_x^2}=-\frac{k}{m}dt\\-\frac{1}{V_x}+\frac{1}{V(0)}=-\frac{k}{m}t\\V_x(t)=\frac{mV_0}{m+kV_0t}[/tex]
[tex]\dot{x}=V_x(t)\\x-x_0=\int_{0}^t{\frac{mV_0}{m+kV_0t}\, dt}=\frac{mV_0}{kV_0}\ln{\frac{m+kV_0t}{m}}\\x=x_0+\frac{m}{k}\ln{\frac{m+kV_0t}{m}}[/tex]
pozdrawiam
