An Object Falling Freely Through the Atmosphere Will Accelerate Due

An object falling freely through the atmosphere will accelerate due to the force of gravity at 9.86 m/s² [Acceleration is the derivative of velocity with respect to time.] The atmosphere, however, will commonly exert a retarding force proportional to the object's velocity squared. The proportionality constant will depend largely on the object's shape. Write and solve the differential equation, then identify a free-falling object's terminal velocity (the limiting velocity) in terms of its drag proportionality constant, k. [To solve explicitly, you may use the initial condition v(0) = 0.]

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