Regarding the behavior of vehicles in roadway traffic typical classes can be identified for individually driven cars showing "collective saturation" features as the capacities of the road are almost maximally utilized, and for an organized group of cars or lorries operating as "convoys" or "platoons". The present paper is devoted to the analysis and adaptive control of a platoon formed of semi-automated vehicles that behaves like a virtual train. It is supposed that the first vehicle plays leading role while the other members have local controllers trained for keeping a safe tracking distance between themselves and the preceding member of the group. In the model investigated the connection between the vehicles acts like an elastic spring with the distinction that no "reaction forces" are applied: the (n+1)th member's motion is influenced by that of the nth member but the members do not affect the motion of the preceding ones. It is supposed that the leading vehicle can freely move, and the aim is to guarantee the possible smoothest motion for the last element of the train that may be followed by various participants of the road communication whose driving comfort has to be kept in mind. (The relative motion of the internal elements of the convoy is regarded as some "interior affair" of no significance.) It is also assumed that the members can communicate with each other to exchange information on their position, velocity, and acceleration data in realtime. The carts are approximately modeled as rigid bodies while their loads are represented by masses connected to their carts by elastic springs of viscous damping. The dynamic interaction between the loads and the carts are not modeled by the controller and the main task of the adaptive control is to compensate the effects of the modeling errors and that of the abandoned internal degrees of freedom. It is shown via computer simulation that the novel, geometrically interpreted adaptive control elaborated at Budapest Tech in the past few years as well as the "acceleration tracking" approach can successfully solve this complicated task.