The vertical shaft skip hoisting system serves as the critical hub for coal mine main transportation. Addressing the characteristic requirement of frequent speed variations in quantitative belt conveyors, this study proposes kinematic calculations to achieve precise control. A trapezoidal acceleration curve control strategy is adopted for speed transition processes. By establishing a kinematic model of the quantitative belt conveyor, this paper systematically analyzes its motion characteristics during low-speed loading phase, high-speed unloading phase, and speed transition phase. The computational formulas for travel distance and time in each operational stage are derived. Through engineering case verification, temporal sequence matching schemes under different feeding positions are validated, providing theoretical foundation for automated collaborative control and optimized design of main shaft hoisting systems in coal mines.