Differential Equation Involving Newtons Law of Motion

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SUMMARY

The discussion centers on solving the differential equation derived from Newton's Law of Motion, represented as mv' = -gm - kv. Participants emphasize the importance of using separation of variables to solve the equation, correcting misconceptions about integrating velocity with respect to time. The correct approach involves rewriting the equation as m dv/(gm + kv) = -dt and integrating both sides to find the position function. Initial conditions at t=0 are also highlighted as crucial for determining the constants involved.

PREREQUISITES
  • Understanding of differential equations
  • Familiarity with Newton's Law of Motion
  • Knowledge of integration techniques, specifically separation of variables
  • Ability to apply initial conditions in mathematical problems
NEXT STEPS
  • Study the method of separation of variables in differential equations
  • Learn about integrating factors and their application in solving linear differential equations
  • Explore the implications of initial conditions in solving differential equations
  • Review the reverse product rule and its relevance in calculus
USEFUL FOR

Students studying physics and mathematics, particularly those focusing on differential equations and their applications in motion analysis.

SparkyEng
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Homework Statement



mv'=-gm-kv

Find the position function using the initial coniditions of t=0 for all Constants

Homework Equations


Reverse product rule



The Attempt at a Solution



My attempt is on my white board. Its attached as a picture.
 

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SparkyEng said:

Homework Statement



mv'=-gm-kv

Find the position function using the initial coniditions of t=0 for all Constants

Homework Equations


Reverse product rule



The Attempt at a Solution



My attempt is on my white board. Its attached as a picture.

You've got some problems there. For example the integral of vdt isn't equal to v*t. v is a function of t. Why don't you try to solve mv'=-gm-kv using separation of variables?
 
From mv'= m dv/dt= -gm- kv, you can get m dv/(gm+kv)= -dt, separating the variables "v" and "t". Integrate both sides of that.
 

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