$22\mathrm{.}1$ A city planner is tasked with designing a sustainable urban transportation system for a rapidly growing metropolitan area. The city is facing challenges related to traffic congestion, air pollution, and limited space for infrastructure expansion. The planner proposes implementing a comprehensive system that integrates various modes of transportation, including public transit, cycling lanes, pedestrian$-$friendly walkways, and innovative technologies.Discuss the key principles, challenges, and potential solutions involved in designing and implementing such a sustainable urban transportation system. In your answer, consider factors such as urban sprawl, population density, land use planning, environmental impact, social equity, economic feasibility, and the role of emerging technologies. Provide examples of successful initiatives from real$-$world cities and analyze their effectiveness in addressing the complex transportation needs of urban populations.