Terminal velocity and drag force in one dimention

In summary, the conversation discusses the velocity of a particle in one dimensional cases and its tendency towards terminal velocity regardless of forces. The equation mv'+bv=F(t) is investigated and it is found that as t tends to infinity, v approaches F(c)/m, where c is some constant. A mathematics theorem is used to support this finding and the notation {f(x)}:b,a represents the definite integral from a to b with respect to x. The theorem appears to be correct, but there is a question about how to determine the value of c.
  • #1
Lucien1011
24
0
In one dimensional cases, will the velocity of a particle tend to the terminal velocity unregardless of any combinations of forces?
I try to investigate this equation: mv'+bv=F(t)
Using the mathematics theorem at the botton, I found that v --> F(c)/m as t tends to infinity. (where c is some constant)

[Thm: if w(x) and u(x) are continuous functions and u(x)>=0, then for a<=x<=b, then {w(x)u(x)}:b,a=w(c)*{u(x)}:b,a for some c lies between a and b]
the notation {f(x)}:b,a represents the definite integral from a to b with repect to x. Sorry for the unusual notation, as I don't know how to type the integral.

Sorry for the poor presentation too. I intended to write the result on a piece of paper and scan it into the computer but my scanner is out of order now.
 
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  • #2
Looks fine to me if the theorem is correct. How are you going to determine the value of c?
 
  • #3
matematikawan said:
Looks fine to me if the theorem is correct. How are you going to determine the value of c?
Oh yeah. I neglect that the upper and lower limit in the thm should be constants.
 
Last edited:

Related to Terminal velocity and drag force in one dimention

1. What is terminal velocity?

Terminal velocity is the maximum speed that an object can reach while falling through a fluid, such as air or water. It occurs when the force of gravity pulling the object down is equal to the drag force pushing against it, resulting in a net force of zero and a constant speed.

2. How is terminal velocity calculated?

Terminal velocity can be calculated using the equation v = √(2mg/ρAC), where v is the terminal velocity, m is the mass of the object, g is the acceleration due to gravity, ρ is the density of the fluid, A is the cross-sectional area of the object, and C is the drag coefficient. This equation takes into account the forces of gravity and drag on the object.

3. What is drag force?

Drag force is the force that opposes the motion of an object through a fluid. It is caused by the collision of the fluid molecules with the surface of the object, and it increases as the speed of the object increases. Drag force is dependent on the density and viscosity of the fluid, as well as the size, shape, and speed of the object.

4. How does drag force affect terminal velocity?

Drag force plays a crucial role in determining an object's terminal velocity. As an object falls through a fluid, its speed increases, resulting in an increase in drag force. At a certain point, the drag force will become equal to the force of gravity on the object, and the object will reach a constant speed known as terminal velocity. If the drag force increases or decreases, the terminal velocity will also change.

5. What factors can affect terminal velocity?

Several factors can affect an object's terminal velocity, including the mass, size, and shape of the object, the density and viscosity of the fluid, and the presence of other forces, such as air resistance or friction. Additionally, altitude and atmospheric conditions can also impact terminal velocity due to changes in air density.

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