The flatcar moves with a constant speed \(v_{0}\) and carries a winch which produces a constant tension \(P\) in the cable attached to the small carriage. The carriage has a mass \(m\) and rolls freely on the horizontal surface starting from rest relative to the flatcar at \(x=0\), at which instant \(X=x_{0}=b\). Apply the work-energy equation to the carriage, first, as an observer moving with the frame of reference of the car and, second, as an observer on the ground. Show the compatibility of the two expressions.

D @ m P X