This paper develops a self-contained framework for studying a mobility-aware intelligent reflecting surface (IRS)-assisted multi-node uplink under simplified but explicit modeling assumptions. The considered system combines direct and IRS-assisted narrowband propagation, geometric IRS phase control with finite-bit phase quantization, adaptive IRS-user focusing based on inverse-rate priority weights, and sequential channel allocation guided by energy detection. The analytical development is restricted to a physics-based two-hop cascaded path-loss formulation with appropriate scaling, an expectation-level reflected-power characterization under the stated independence assumptions, and the exact chi-square threshold for energy detection, together with its large-sample Gaussian approximation. A MATLAB implementation is used to generate a sample run, which is interpreted as a numerical example. This work is intended as a consistent, practically-aligned baseline to support future extensions involving richer mobility models or more advanced scheduling policies.