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This lecture covers the concepts of trajectory and velocity in advanced physics, focusing on rectilinear motion. It discusses the relationship between displacement, velocity, and acceleration, as well as the properties of derivatives. The lecture also explores the equations for velocity and acceleration, emphasizing the importance of instantaneous velocity. Key topics include the graphical representation of motion, the derivation of fundamental derivatives, and the interpretation of acceleration from velocity. The lecture concludes with a detailed analysis of instantaneous velocity and acceleration, highlighting their significance in understanding motion.