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Community Answer

【General guidance】The answer provided below has been developed in a clear step by step manner.Step1/3Diagram showing the forces acting on the marble as it sinks in the honey: ^ positive direction | |<----Frictional force (Ff) |----> |<----Buoyant force (Fb) |----> |<----Weight of marble (mg) |----> | v Let v(t) be the velocity of the marble at time t. The differential equation modelling the velocity of the marble is: \( \mathrm{{m}\times{d}\frac{{v}}{{\left.{d}{t}\right.}}={m}{g}-{F}{b}-{F}{f}} \)where m is the mass of the marble, g is the acceleration due to gravity, and Fb and Ff are the buoyant force and frictional force, respectively.Explanation:Please refer to solution in this step.Step2/3The equilibrium solution of the differential equation is found by setting \( \mathrm{{d}\frac{{v}}{{\left.{d}{t}\right.}}} \) to zero:\( \mathrm{{m}{g}-{F}{b}- ... See the full answer