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In this lecture, Aramboy discusses the application of differential equations in mechanics, focusing on the motion of objects in fluid with resistive forces. While free fall problems typically neglect air resistance, it actually affects the motion of falling bodies, as seen with skydivers reaching terminal velocity. By using Newton's second law of motion, a differential equation is derived to describe the velocity of the object over time. This allows for the calculation of total distance traveled and determination of altitude for skydivers.
