A gas-filled pneumatic strut in an automobile suspension system behaves like a piston-cylinder apparatus. At one instant when the piston is L=0 15 maway from the closed end of the cylinder, the gas density is uniform at ρ=18 kg m3 and the piston begins to move away from the closed end at V =12m s. Assume as a simple model that the gas velocity is one-dimensional and proportional to distance from the closed end; it varies linearly from zero at the end to u=V at the piston. Find the rate of change of gas density at this instant. Obtain an expression for the average density as a function of time.