How Do You Model Instantaneous Velocity in a Fluid with Square Root Drag?

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The discussion focuses on modeling the instantaneous velocity of an object experiencing drag in a fluid, described by the equation -k(v^1/2). The user attempts to derive the velocity equation using the net force and drag force, leading to a differential equation. They express confusion regarding the resulting equation, which suggests increasing velocity over time, contradicting expected deceleration. Other participants clarify that if only drag acts on the object, it should decelerate, and they suggest incorporating an integration constant to correctly apply initial conditions. The conversation emphasizes the importance of correctly modeling forces to derive an accurate expression for instantaneous velocity.
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Homework Statement


An object dragged through an unknown fluid experiences a force opposite to that of its initial velocity (Vi) that is equal to -k(v^1/2). find the equation that models its instantaneous velocity

Fn = Force Net
Ff = Frictional force
Vi = Initial Velocity
V = instantaneous velocity

Homework Equations


Fn=ma
Ff=-k(v^1/2)


The Attempt at a Solution



Fn=Ff
ma=-k(v^1/2)
dv/dt=(-k/m)(v^1/2)
S[dv/(v^1/2)]=(-k/m)S[dt]
2(v^1/2)=-kt/m
v=(-kt/2m)^2 + Vi

which can't be right because that would mean velocity increased as time moves positively...

i'm lost. help lol
v=
 
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Does the object have mass m? Is another force being applied to the object?

If the force is subject only to drag, then it will deceleration in proportion to kv1/2 according to the problem as stated.

If the mass falls under gravity then the mass will decelerate or even accelerate to a constant velocity where the drag force = the force of gravity.

a = dv(t)/dt = F(t)/m, where F(t) = applied force - drag force,

and the initial condition is v(t=0) = vi/.
 
there is no mass stated and the object is traveling horizontally and not subject to gravity.

i guess I'm having trouble deriving a velocity equation more than i am having trouble understanding the situation. I'm not even sure if the way i tried it first is the right way.

all i know for sure is that the only force acting on the point is -kv^(1/2)

could u perhaps help me find an equation for its instantaneous velocity with respect to time?
 
S[e^x]=f(u)^n;1461783 said:

Homework Statement


An object dragged through an unknown fluid experiences a force opposite to that of its initial velocity (Vi) that is equal to -k(v^1/2). find the equation that models its instantaneous velocity

Fn = Force Net
Ff = Frictional force
Vi = Initial Velocity
V = instantaneous velocity

Homework Equations


Fn=ma
Ff=-k(v^1/2)


The Attempt at a Solution



Fn=Ff
ma=-k(v^1/2)
dv/dt=(-k/m)(v^1/2)
S[dv/(v^1/2)]=(-k/m)S[dt]
2(v^1/2)=-kt/m

you need to add a constant here:

2(v^1/2)=-kt/m + C

then

v^1/2=-kt/2m + D


v=(-kt/2m)^2 + 2(-kt/2m)D + D^2

So know solve for D using initial conditions.
 
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