The Velocity in terms of time and drag K

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SUMMARY

The discussion focuses on the mathematical modeling of a body falling into a viscous liquid, where the velocity decreases proportionally to its current velocity. The initial velocity is set at 30 m/s, with a proportionality constant k of 0.3 m/s². The equation governing the motion is derived as a = -kv, indicating that acceleration is inversely related to velocity. The integration of this equation over the time interval from 0 to 0.25 seconds is explored to solve for the velocity function.

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  • Knowledge of proportional relationships in physics
  • Basic concepts of kinematics
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Physics students, engineers, and anyone interested in the dynamics of motion in viscous fluids will benefit from this discussion.

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A body falls into viscous liquid which causes the velocity to decrease at the rate proportional to the velocity.
v=velocity(m/s)
t=time(s)
k= constant of proportionality
The initial velocity of the body=30m/s
k=0.3m/s^2
t=0.25s
Solve for v in terms of t and k



First step possible: a=-kt then first order of integration t1=0;t2=0.25s

int a dt ?

But where is g (means g-kt)??
 
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see that rate is proportional to velocity, not time.

so a = -kv
 

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