Cycling has become increasingly important on German roads over the past 20 years. However, the number of crashes involving cyclists, which may go along with severe injuries or fatalities, is increasing. Between 2010 and 2018 the number of killed cyclists increased from 381 to 445 (+16.8%). The interaction of right-turning motorists with passing cyclists is one of the most critical ones, particularly if the cyclist is relatively behind the motorist (i.e., in its blind spot). Advanced driver assistance systems (ADAS) are being developed in order to assist in potential critical situations before they evolve to crashes. Infrastructure-based, cooperative solutions could inform or warn road users before a potential collision via V2X or a roadside entity, such as a dedicated traffic light. The Bike Flash system is an example of such a solution. Its drawback is that it warns if a cyclist is present without considering the possible outcome of the situation (e.g., dangerous or not), which can lead to acceptance problems. Thus, in an algorithm was developed and successfully tested, capable of sending out warnings if a potential crash was predicted. For this purpose, a construction traffic light, called “amber light” (AL), was used to inform the right-turning motorists about potential collisions. This method is based on a decision tree (DT) considering the distances of the interacting cyclists and motorists to their collision/conflict point (CP), their speeds and the predicted post encroachment time (pPET), which continuously quantifies to what extent two interacting partners will miss each other. Interestingly, the acceleration functions of the road users are not part of the DT, although they are—except the change of direction—the only control parameters to realise evasive actions. Further, it is not clear, at what distance to the CP crash warnings are reliable and thus, where such an AL should be installed. We will address these open aspects by analysing the acceleration functions of cyclists and motorists in unaffected, uncritical and critical encounter situations in the time and frequency domains. We will emphasize the importance of acceleration functions distinguishing between critical and uncritical encounters in certain distances before the CP. Furthermore, we will show that critical encounters of cyclists and uncritical encounters of motorists show completely different characteristics, and we will try to measure surprise (or anticipation) by applying the entropy metric on the acceleration functions and conduct inference statistical tests. In terms of reliability and location of such a warning system before the CP we will compute pPET while considering kinematic patterns of the road users. These are examples of some of the essentially important aspects to establish well-accepted cooperative warning systems in the future.