My research project focuses on the role of motility and nutrients in bacterial competition and colony formation. Bacterial motility has two types of mechanisms - directed movement (chemotaxis) and undirected movement. Motivated by a series of petri dish experiments, we study undirected bacterial movement which was rarely considered in literature. We use different nutrient media such as agar and liquid in the theoretical framework to discuss the results of competition and colony formation. The consistency of our numerical simulations and experimental data illustrates the existence of undirected motility in bacteria.