The Test of Understanding Graphs in Kinematics (TUG-K) is a multiple-choice test developed by Beichner in 1994 to assess students' understanding of kinematics graphs. Many of the items on the TUG-K have strong distractor choices which correspond to students' common difficulties with kinematics graphs. Instruction is unlikely to be effective if instructors do not know the common difficulties of introductory physics students and explicitly take them into account in their instructional design. We evaluate one aspect of the pedagogical content knowledge of first-year physics graduate students enrolled in a teaching assistant training course related to topics covered in the TUG-K. In particular, for each item on the TUG-K, the grad. students were asked to identify which incorrect answer choice they thought would be most commonly selected by introductory physics students if they did not know the correct answer after instruction in relevant concepts. We used the grad. student data and the data from Beichner's original paper for introductory physics students (which was collected from over 500 college and high school students) to assess this aspect of the pedagogical content knowledge of the grad. students, i.e., knowledge of student difficulties related to kinematics graphs as they are revealed by the TUG-K. We find that, although the grad. students, on average, performed better than random guessing at identifying introductory student difficulties on the TUG-K, they did not identify many common difficulties that introductory students have with graphs in kinematics. In addition, we find that the ability of grad. students to identify the difficulties of introductory students is context dependent and that discussions among the grad. students improved their understanding of student difficulties related to kinematics graphs. Moreover, we find that the ability of American grad. students in identifying common student difficulties is comparable with that of foreign grad. students.