A rocket sled traveling on a horizontal track is slowed by a retro-rocket fired in the direction of travel. The initial speed of the sled is \(U_{0}=500 \mathrm{~m} / \mathrm{s}\). The initial mass of the sled is \(M_{0}=1500 \mathrm{~kg}\). The retro-rocket consumes fuel at the rate of \(7.75 \mathrm{~kg} / \mathrm{s}\), and the exhaust gases leave the nozzle at atmospheric pressure and a speed of \(2500 \mathrm{~m} / \mathrm{s}\) relative to the rocket. The retro-rocket fires for \(20 \mathrm{~s}\). Neglect aerodynamic drag and rolling resistance. Obtain and plot an algebraic expression for sled speed \(U\) as a function of firing time. Calculate the sled speed at the end of retro-rocket firing.