Determine the Velocity of the body with Velocity decreasing by v^2 = k/s

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SUMMARY

The discussion focuses on determining the velocity of a body under the influence of a retarding force, described by the equation v² = k/s, where k is a constant. Given an initial speed of 1.8 in/sec and a position of 9.2 in at time t=0, the goal is to find the speed v at t=4.0 seconds. The solution approach involves calculating k, deriving the position function s(t) using the initial conditions, and substituting this into the velocity equation to find v at the specified time.

PREREQUISITES
  • Understanding of differential equations and their applications in motion.
  • Familiarity with the concept of retarding forces in physics.
  • Knowledge of initial value problems and boundary conditions.
  • Proficiency in calculus, specifically integration and differentiation.
NEXT STEPS
  • Study the derivation of motion equations under retarding forces.
  • Learn about solving initial value problems in differential equations.
  • Explore the application of boundary conditions in physics problems.
  • Investigate the relationship between velocity, acceleration, and position in motion analysis.
USEFUL FOR

This discussion is beneficial for physics students, educators, and anyone interested in understanding motion dynamics under retarding forces, particularly in the context of differential equations and initial value problems.

Northbysouth
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Homework Statement


A retarding force is applied to a body moving in a straight line so that, during an interval of its motion, its speed v decreases with increased position s according to the relation v2=k/s, where k is a constant. If the body has a forward speed of 1.8 in/sec and its position coordinate is 9.2 in at time t=0, determine the speed v at t=4.0 sec.


Homework Equations



v = ds/dt

The Attempt at a Solution



I'm honestly not sure how to start this question. Suggestions would be appreciated.
 
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I would start with v = √(k/s) = ds/dt. k is easily gotten. Then get s(t) with the known boundary value, and finally substitute v = √(k/[s(t=4)].

Hope that puts you on the right track.
 

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