Velocity as a function of time -- Terminal Velocity

In summary, the conversation revolved around solving a physics problem using Euler's Method, which requires finding the velocity as a function of time (v(t)). The problem involves a parachute and a drag force, and the goal is to plot the v(t) curves for different initial velocities. The conversation also touched on the confusion about where to insert time (t) in the equation and the importance of understanding Euler's Method before attempting to solve the problem.
  • #1
alex steve
5
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I am having trouble finding a staring place. My class requires us to use python to solve the equation.

This problem requires me to use eulers method to solve it. My issues is that i am getting confused as of how to find the v(t). Its been a while since i have had to do advance physics like this. Any help would be appreciated.

The question asks:

When jumping from an airplane, you will most often have a parachute to slow your fall. Here let's consider a very simple example in which the frictional drag force is linearly dependent on the velocity:dv/dt=a−bvwhere a and b are constants. In our case a corresponds to the acceleration due to gravity, and b is a constant from drag. Note that the drag force is negative, indicating it opposes the motion. Use the Euler method to solve for v as a function of time and plot your results. A convenient choice of parameters is a=10and b=1. You should find that v approaches a constant value at long times: this is the terminal velocity. If you open your chute immediately after jumping from the plane, you will have vinitial∼1 m/s, but if you wait a minute or so, you will have vinitial∼50 m/s. Plot both v(t) curves on the same plot with a legend.

I am just getting confused with : if the equations says dv/dt = a=bv , where would i insert t for v(t) if the equation has no t except for the dt in the denominator.
 
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  • #2
Please don't delete the homework template.
alex steve said:
I am just getting confused with : if the equations says dv/dt = a=bv , where would i insert t for v(t) if the equation has no t except for the dt in the denominator.
It is a differential equation, you have to solve it first.
 
  • #3
alex steve said:
I am just getting confused with : if the equations says dv/dt = a=bv , where would i insert t for v(t) if the equation has no t except for the dt in the denominator.
First, what do you know about Euler's Method?
 
  • #4
I do not need to know about Euler's method right now . I just need help on figuring out the v(t) equation which is the first step of this problem. I will have to code The euler's method later on.
 
  • #5
alex steve said:
I do not need to know about Euler's method right now . I just need help on figuring out the v(t) equation which is the first step of this problem. I will have to code The euler's method later on.
You won't have a v(t) equation. You'll have a dv/dt equation (which you already have). Then you'll apply Euler's Method to that. So you really should read up on Euler's method first. A web search should turn up many references and examples of its application.
 

FAQ: Velocity as a function of time -- Terminal Velocity

1. What is terminal velocity?

Terminal velocity is the maximum speed that an object can reach when falling through a fluid, such as air or water. It occurs when the force of gravity pulling the object down is equal to the opposing force of air resistance pushing the object up.

2. How is terminal velocity calculated?

Terminal velocity is 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 object's cross-sectional area, and C is the drag coefficient.

3. What factors affect terminal velocity?

The factors that affect terminal velocity include the mass and shape of the object, the density and viscosity of the fluid, and the force of gravity. Objects with a larger mass and surface area will have a higher terminal velocity, while a denser or more viscous fluid will result in a lower terminal velocity.

4. Can an object exceed its terminal velocity?

No, an object cannot exceed its terminal velocity. As an object falls faster, the air resistance increases until it balances out with the force of gravity, resulting in a constant terminal velocity. This is known as a state of dynamic equilibrium.

5. How does altitude affect terminal velocity?

Altitude can affect terminal velocity because air density decreases with altitude. This means that at higher altitudes, the air is less dense and there is less air resistance, resulting in a higher terminal velocity. However, other factors such as gravitational force and the object's mass and shape still play a role in determining the specific terminal velocity at a given altitude.

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