How Long to Reach Half Terminal Speed with Air Resistance?

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SUMMARY

The discussion focuses on calculating the time it takes for an object to reach half of its terminal speed when falling under the influence of air resistance. The air resistance is modeled by the equation F = -bv, where b is the proportionality constant. The relevant equations include a = g - (bv/m) and a = dv/dt, leading to a differential equation that needs to be solved for v and t. Participants are encouraged to derive and solve this differential equation to find the solution.

PREREQUISITES
  • Understanding of Newton's second law of motion
  • Familiarity with differential equations
  • Knowledge of terminal velocity concepts
  • Basic calculus skills for solving differential equations
NEXT STEPS
  • Derive the differential equation from a = g - (bv/m)
  • Learn techniques for solving first-order linear differential equations
  • Study the concept of terminal velocity in physics
  • Explore numerical methods for approximating solutions to differential equations
USEFUL FOR

Students studying physics, particularly those focusing on mechanics and dynamics, as well as educators and tutors looking to enhance their understanding of motion under air resistance.

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Homework Statement


An object of mass m falls from rest subject to air resistance force directly proportional to the object's speed, F=-bv, where b is the proportionality constant in N/(m/s) and the negative sign indicates the direction of the force opposite to the direction of the velocity. How long does it take this object to reach half of its terminal speed?


Homework Equations



a=g-bv/m, a=dv/dt, etc...

The Attempt at a Solution


tried, all failed.
 
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Using the two equations you posted, and eliminating a between them, should give you a differential equation involving v and t. What is it? Can you solve it?
 

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