## 4 Discussion  
The purpose of this study was to explore the relationship between IMTPF, sprint mechanics, and linear acceleration performance. Our main findings revealed large correlations between IMTPF and v\({}_{0}\), and moderate to large relationships between IMTPF and sprint times from 15 to 30 m distance intervals, thus supporting the initial hypothesis. The relationship between IMTPF and the v\({}_{0}\) indicates that the maximal vertical force capacity of lower limbs, assessed during isometric contractions, is correlated with the sprint-running maximal velocity capability of the athlete, as well as with the capacity to generate  
Figure 1: Linear relationships and coefficient of determination (R\({}^{2}\)) between isometric mid-high pull maximal force and F\({}_{0}\) (**A**), v\({}_{0}\) (**B**), and P\({}_{\max}\) (**C**). Figure 2: Linear relationships and coefficient of determination (R\({}^{2}\)) between isometric mid-high pull maximal force and time to 5 m (**A**), time to 10 m (**B**), time to 15 m (**C**), time to 20 m (**D**), time to 25 m (**E**), and time to 30 m (**F**). horizontal force at high running velocities, particularly during the late acceleration phase. Furthermore, the observed inverse relationships between IMTPF and sprint acceleration performance further suggest that the capacity to generate peak vertical force may be compromised toward the late acceleration phase (>15 m). Associations between IMTPF and late acceleration performance have previously been reported [15; 19; 20; 21]. In contrast, the variables that represent the early acceleration phase (F\({}_{0}\), time to 5 m and 10 m) were not significantly related to IMTPF. The latter may be attributed by the differences in the orientation of the force vector during the early and late acceleration phases. Specifically, the early and late acceleration phases differ in the generation and application of horizontal and vertical forces. During the early acceleration phase, the primary focus is on generating high amounts of horizontal force to overcome inertia and propel the body forward. In this phase, only the horizontal component of the total force contributes to the forward displacement of the body mass, meaning the vertical component does not contribute to forward acceleration, though it remains essential for stabilizing the body to keep moving forward [32]. Additionally, the early phase is mechanically characterized by the activation of the knee and hip extensor muscles, in conjunction with the calf muscles, to generate propulsion during the support phase of the step cycle. Moreover, the larger contact time allows for a longer duration of force application, approximately 200 ms, compared to 100 ms during the maximum velocity phase. Conversely, the late acceleration phase is mechanically characterized by an increase in both step length and frequency, accompanied by a continuous rise in running velocity. This higher speed is associated with a reduction in ground contact time, leading to significant changes in kinetic patterns. During this phase, the relative proportion of horizontal to vertical force decreases, and the orientation of the force vector becomes increasingly vertical [2; 32]. Kinematically, this transition in force direction could be explained by the decrease in forward trunk lean as velocity increases, ultimately culminating in an almost upright posture [33; 34]. These findings are not in line with previous studies that reported relationships between isometric strength and initial sprint performance in male athletes [15; 19; 20]. However, it is important to note the methodological differences between the current study and the research conducted by [PERSON] et al. In the aforementioned study, basketball players were allowed to self-select their hip and knee angles in order to assume the second pull weightlifting position [20]. Furthermore, the contact time during the support phase of the step cycle is higher in basketball players compared to sprinters, allowing additional time to develop force. Additionally, [PERSON] et al.