30. A mass m falls under gravity (force mg) through a liquid whose viscosity is decreasing so that the retarding force is -2mv/(1+t), where u is the speed of m. If the mass starts from rest, find its speed, its acceleration, and how far it has fallen (in terms of g) when t = 1.
30. A mass m falls under gravity (force mg) through a liquid whose viscosity is decreasing so that the retarding force is -2mv/(1+t), where u is the speed of m. If the mass starts from rest, find its speed, its acceleration, and how far it has fallen (in terms of g) when t = 1.
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Transcribed Image Text:30.
A mass m falls under gravity (force mg) through a liquid whose viscosity is decreasing
so that the retarding force is -2mv/(1+t), where v is the speed of m. If the mass
starts from rest, find its speed, its acceleration, and how far it has fallen (in terms
of g) when t = 1.
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Step 1: Define Newton's second law of motion:
VIEWStep 2: Find the differential equation for the given problem:
VIEWStep 3: Find the general solution of the equation (5):
VIEWStep 4: Find the speed as a function of time:
VIEWStep 5: Find the speed at t=1:
VIEWStep 6: Find the acceleration at t=1:
VIEWStep 7: Find the vertical distance covered by the mass from its initial position when t=1.
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