- #31
oddjobmj
- 305
- 0
Nevermind! Ah, I forgot C is actually positive. That worked.
Thank you both!
Thank you both!
Function of force with respect to v & t; find final v and distance
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SUMMARY
The discussion centers on solving the motion of a particle subjected to a force defined by F(v,t) = -βv²e^(-αt), where α = 0.27 s⁻¹ and β = 1.19 kg/m. Participants clarified the relationship between acceleration, velocity, and force, emphasizing the need to integrate the acceleration function to derive velocity. The final velocity was determined to be approximately 0.217 m/s, while the distance traveled at t = 10 seconds was calculated to be around -1.68 meters. The discussion highlighted common pitfalls in applying calculus to physics problems, particularly in determining constants of integration.
PREREQUISITES- Understanding of Newton's second law (F = ma)
- Knowledge of calculus, specifically integration and differentiation
- Familiarity with exponential decay functions
- Ability to manipulate algebraic expressions involving constants
- Study the method of separation of variables in differential equations
- Learn about integrating factors for solving first-order linear differential equations
- Explore the implications of negative constants in physical equations
- Review the concepts of initial conditions and their role in determining constants of integration
Students of physics, particularly those studying mechanics and calculus, as well as educators looking for examples of applying differential equations to real-world problems.