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While automated vehicles (AVs) are expected to revolutionize future transportation systems, emerging AV technologies open a door for malicious actors to compromise intelligent vehicles. As the first generation of AVs, adaptive cruise control (ACC) vehicles are vulnerable to cyberattacks. While recent effort has been made to understanding the impact of attacks on transportation systems, little work has been done to systematically model and characterize the malicious nature of candidate attacks. In this study, we develop a general framework for modeling and synthesizing two types of candidate attacks on ACC vehicles, namely direct attacks on vehicle control commands and false data injection attacks on sensor measurement, with explicit characterization of their adverse effects. Based on linear stability analysis of car-following dynamics, we derive a series of analytical conditions characterizing the malicious nature of potential attacks. This ensures a higher degree of realism in modeling attacks with adverse effects, as opposed to simply considering attacks as constants or random variables. Notably, the conditions derived provide an effective method for strategically synthesizing an array of candidate attacks on ACC vehicles. We conduct extensive simulation to examine the impacts of intelligently designed attacks on microscopic car-following dynamics and macroscopic traffic flow. Numerical results illustrate the mechanism of candidate attacks, offering useful insights into understanding the vulnerability of future transportation systems. The methodology developed allows for further study of the widespread impact of strategically designed attacks on traffic cybersecurity, and is expected to inspire the development of efficient attack detection techniques and advanced vehicle controls.