Find the constant of motion

Consider a particle with mass $m=3~\text{g}$ that can move on the x-axis and interacts with a wave moving to right with speed $u=1000~ \text{m}/\text{s}$. The interaction energy between the particle and the wave is given by $V(x-u t)$ where $V(x)$ is an unknown function. Because the interaction energy is time-dependent the usual total energy of the particle $E(t)= \frac{m \dot{x}^2}{2}+V(x-u t),$ is not conserved. That is, $\frac{dE(t)}{dt}\neq 0$. Nonetheless, one can show that for certain $\beta$ the quantity $I(t)=\frac{m\dot{x}^2}{2}+V(x-ut)-\beta \dot{x}$ is conserved, i.e., $\frac{dI(t)}{dt}=0$. Find $\beta$ in kg m/s.