Background: While educators strive for optimal student motivation to enhance the quality of learning for all, different students attending the same course can have different needs. Person-centered approaches on basic needs profiles, categorizing individuals into groups with similar motivational profiles, have the potential to inform the relationship between different variables per cluster and to support instructional design sensitive to student differences. However, they are still absent in engineering education research (EER). Purpose/Hypothesis: This gap is addressed by analyzing the basic psychological needs of engineering students as potential mediators during a mandatory, first-year course on the ethics and history of technology. The aims are thus to (1) determine whether distinct basic needs profiles can be identified and (2) investigate how students' motivation differed and evolved during the course for the different basic needs profiles. Design/Methods: Two-step cluster analyses, MANOVA, and t-test analyses were conducted using the data collected from 1864 students with digital questionnaires completed at three points within a semester of a course. Results: We construed four student profiles from the survey data based on the distinct roles of competence and autonomy, with post hoc tests showing relationships between meaningful differences in evaluation of course elements, motivation, course appreciations, and motivation dynamics. Conclusions: The person-centered approach is promising in engineering education design to answer differences in students' basic needs to improve the quality of learning for all. We showed that the person-centered approach could also add important insights complementary to the variable-centered approach in EER on dynamics of motivation for learning.