For efficient and effective pedagogical interventions to address Uganda's alarmingly poor performance in Physics, it is vital to understand students' motivation patterns for Physics learning. Latent profile analysis (LPA)--a person-centred approach--can be used to investigate these motivation patterns. Using a three-step approach to LPA, we sought to answer the following research questions: RQ1, which profiles of secondary school students exist with regards to their motivation for Physics learning; RQ2, are there differences in students' cognitive learning strategies in the identified profiles; and RQ3, does students' gender, attitudes, and individual interest predict membership in these profiles? The sample comprised 934 Grade 9 students from eight secondary schools in Uganda. Data were collected using standardised questionnaires. Six motivational profiles were identified: (i) "low-quantity" motivation profile (101 students; 10.8%); (ii) "moderate-quantity" motivation profile (246 students; 26.3%); (iii) "high-quantity" motivation profile (365 students; 39.1%); (iv) "primarily intrinsically motivated" profile (60 students, 6.4%); (v) "mostly extrinsically motivated" profile (88 students, 9.4%); and (vi) "grade-introjected" profile (74 students, 7.9%). "Low-quantity" and "grade-introjected" motivated students mostly used surface learning strategies whilst the "high-quantity" and "primarily intrinsically" motivated students used deep learning strategies. Lastly, unlike gender, individual interest and students' attitudes towards Physics learning predicted profile membership. Teachers should provide an interesting autonomous Physics classroom climate and give students clear instructions in self-reliant behaviours that promote intrinsic motivation.