Calculating Drag Force on Boat: Speed as Function of Time

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SUMMARY

The discussion focuses on calculating the drag force acting on a fishing boat as it drifts after shutting off its engines. The drag force is defined by the equation F = -kv², where k is a constant related to drag. The user attempts to derive the boat's speed as a function of time by applying Newton's second law, F = ma, leading to the acceleration equation a = -kv²/m. The challenge lies in expressing velocity v as a function of time t without it appearing in the function itself, prompting the suggestion to replace acceleration with its equivalent dv/dt.

PREREQUISITES
  • Understanding of Newton's second law (F = ma)
  • Familiarity with calculus, specifically integration and differentiation
  • Knowledge of drag force concepts in fluid dynamics
  • Basic physics principles related to motion and forces
NEXT STEPS
  • Study the derivation of velocity as a function of time in drag force scenarios
  • Learn about differential equations and their applications in motion problems
  • Explore numerical methods for solving ordinary differential equations (ODEs)
  • Investigate the effects of varying drag coefficients on boat speed
USEFUL FOR

Physics students, engineers, and anyone interested in fluid dynamics and motion analysis, particularly in the context of marine vehicles.

datapirate42
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F = -kv2

A fishing boat of mass m moves through the water in the +x direction. At time = 0 and x=0 it shuts its engines off and begins to drift. It experiences drag according to the above equation, calculate the boat's speed as a function of time.

I've tried taking F = ma
so a = -kv2/m

now v should be the integral of that with respect to time
my problem is getting v as a function of t without it being in that function itself
 
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Hint: Replace a with its equivalent dv/dt.
 

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