Solving for Velocity of Falling Object with Air Resistance

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SUMMARY

The discussion focuses on calculating the velocity of a falling object with air resistance, specifically a 25-pound mass experiencing a decelerating force proportional to its velocity. The formula v(t) = (mg/b)t - (m^2*g / b^2) + m/b*vknot was suggested but caused confusion among participants. The correct approach involves using Newton's laws and deriving a differential equation to model the forces acting on the object. Participants emphasized the need for clarity in the problem statement, particularly regarding the forces involved.

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  • Understanding of Newton's laws of motion
  • Familiarity with differential equations
  • Basic knowledge of forces and motion
  • Concept of air resistance and its mathematical representation
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  • Study the derivation of differential equations in physics
  • Learn how to apply Newton's second law to falling objects
  • Explore the concept of air resistance and its effects on motion
  • Investigate numerical methods for solving differential equations
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Students in physics, educators teaching mechanics, and anyone interested in understanding the dynamics of falling objects with air resistance.

rlagustn
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Warning: Homework Template must be used for questions posted in the Homework area.
An object with a mass if falling with a force that is equal to its own weight of 25 pounds. The air resistance causes a decelerate force equal to 1/2 the velocity of the object at any time. If the object falls from rest, what is the velocity of the object after 8 seconds?

I'm just confused at the wordings of the question. I just cannot find a way to start.
I tried to use to formula v(t) = (mg/b)t - (m^2*g / b^2) + m/b*vknot but the formula did not make sense to me. I was wondering if there are any other formulas I could use to solve this problem.
 
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I'm just confused at the wordings of the question. I just cannot find a way to start.
Start with a free body diagram - draw all the forces on the object, the use Newton's laws.
You'll end up with a differential equation.
 
rlagustn said:
An object with a mass if falling with a force that is equal to its own weight of 25 pounds. The air resistance causes a decelerate force equal to 1/2 the velocity of the object at any time. If the object falls from rest, what is the velocity of the object after 8 seconds?

I'm just confused at the wordings of the question. I just cannot find a way to start.
It is confusing. "Falling with a force" does not make much sense.
And a force equal to 1/2 the velocity it's definitely nonsense. The units do not match.
Is this the actual text of the problem?
 

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