Use seperation of varibles to Find velocity interms of time

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SUMMARY

The discussion focuses on using separation of variables to derive the velocity of a mass \( m \) experiencing a drag force \( f(v) = -cv^{3/2} \). The initial velocity is \( V_0 \) at time \( t = 0 \). Participants confirm that the correct approach involves rearranging the equation \( F(v) = m \frac{dv}{dt} \) to isolate \( dv \) and \( dt \) before integrating. To determine the time at which the mass stops, the velocity \( v \) should be set to zero.

PREREQUISITES
  • Understanding of Newton's second law of motion
  • Familiarity with calculus, specifically integration techniques
  • Knowledge of drag forces and their mathematical representation
  • Basic concepts of differential equations
NEXT STEPS
  • Study the application of separation of variables in differential equations
  • Learn about drag force models in physics, particularly \( f(v) = -cv^{3/2} \)
  • Explore integration techniques for solving first-order ordinary differential equations
  • Investigate the implications of initial conditions in motion problems
USEFUL FOR

Students studying physics, particularly those focusing on mechanics and differential equations, as well as educators looking for examples of applying calculus to real-world problems involving motion and forces.

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Homework Statement


A mass m has a velocity Vo at time t=0 and coasters along the x-axis were the drag force is f(v)=-cv ^3/2 find v in terms of t and the other given parameter. at what time will it stop.


Homework Equations


F(v)=m dv/dt


The Attempt at a Solution


So i started by using separation of var and got dv= f(v)dt/m then i just take the integral of both sides Is this correct? then i just do it from 0 to t to one side and 0 to v to the other? How would i then find what time it would stop? set v = 0 or something?

Thanks
 
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Correct on all accounts. Just make sure that anything with v in it is on the left side and anything with t in it is on the right before you integrate.
 

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