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Problem 3: An object of mass m at the origin has an initial velocity vo in the + direction at time t = 0, and moves along the + axis through a substance where there is a drag force F(v) = -cv¹/³ (i.e., something intermediate between viscous and aerodynamic drag). (a) Use the separation of variables method to integrate the equation of motion and find v(t). (b) At what time will the mass come to rest? (c) Use the chain-rule substitution v = v dv/dr in the equation of motion, and solve to find v(x). Show that the mass eventually travels a distance 3mv2/3/2c. For each part, check your result for dimensional consistency and limiting-case behavior.

Problem 3: An object of mass m at the origin has an initial velocity vo in the + direction at time t = 0, and moves along the + axis through a substance where there is a drag force F(v) = -cv¹/³ (i.e., something intermediate between viscous and aerodynamic drag). (a) Use the separation of variables method to integrate the equation of motion and find v(t). (b) At what time will the mass come to rest? (c) Use the chain-rule substitution v = v dv/dr in the equation of motion, and solve to find v(x). Show that the mass eventually travels a distance 3mv2/3/2c. For each part, check your result for dimensional consistency and limiting-case behavior.

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Problem 3: An object of mass m at the origin has an initial velocity vo in the + direction at time t = 0, and moves along the + axis through a substance where there is a drag force F(v) = -cv¹/³ (i.e., something intermediate between viscous and aerodynamic drag). (a) Use the separation of variables method to integrate the equation of motion and find v(t). (b) At what time will the mass come to rest? (c) Use the chain-rule substitution v = v dv/dr in the equation of motion, and solve to find v(x). Show that the mass eventually travels a distance 3mv2/3/2c. For each part, check your result for dimensional consistency and limiting-case behavior.
Transcribed Image Text:Problem 3: An object of mass m at the origin has an initial velocity vo in the + direction at time t = 0, and moves along the + axis through a substance where there is a drag force F(v) = -cv¹/³ (i.e., something intermediate between viscous and aerodynamic drag). (a) Use the separation of variables method to integrate the equation of motion and find v(t). (b) At what time will the mass come to rest? (c) Use the chain-rule substitution v = v dv/dr in the equation of motion, and solve to find v(x). Show that the mass eventually travels a distance 3mv2/3/2c. For each part, check your result for dimensional consistency and limiting-case behavior.
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