Background: Many studies have shown that muscle power (power = velocity × strength) is a critical determinant of physical tasks, such as gait and sit to stand, in older adults. However, it is still unclear whether velocity or strength has a stronger effect on physical tasks. This study aimed to examine the relative importance of velocity and strength components in determining inter-individual differences in gait and sit-to-stand tasks. Methods: The participants were 43 female older adults who were residing in geriatric health service facilities (mean age 87.4 years). We measured participants' gait speed, sit-to-stand ability using the five-times sit-to-stand test, movement velocity of knee extension, and quadriceps strength. Results: Gait speed was significantly associated with movement velocity (r = 0.38; p = 0.013), but there was no significant association with quadriceps strength. Movement velocity was selected as the independent variable for gait speed in multiple regression analysis. The five-times sit-to-stand test result was not significantly associated with movement velocity, but it was significantly associated with quadriceps strength (r = -0.50; p = 0.016). Quadriceps strength was selected as the independent variable for sit to stand in multiple regression analysis. Conclusions: The results suggest that the relative importance of velocity and strength components varies depending on the physical task. These differences may be attributed to the intensity of the physical task.