Finding velocity as a function of time

In summary: Then you integrate both sides to get the solution. In summary, the conversation is about finding a differential equation for the velocity of a ball thrown with initial velocity v° and air resistance given by F = -kv. After setting up the equation and rearranging it, the person is unsure of how to proceed and suggests trying to invert both sides and then integrating to find the solution. They are also unsure about the inverse method and ask for clarification.
  • #1
Mmarzex
2
0
Okay so the problem is that we have the case of a ball being thrown up at initial velocity v° with air resistance expressed as F = -kv where k is a constant acting on it. We are suppose to find a differential equation for the velocity at a given point as a function of time. So I started with
ƩF = ma
- mg - kv = ma

Then I moved everything around to get
dv/dt = (-mg - kv)/m

Now we have never done a solution like this in my AP Physics class so I am rather at a lose. I know that I need to get it so that dv and v are on the same side but I'm not really sure how to go about that so that I can integrate the whole equation to get the solution.
 
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  • #2
Try inversing both sides
 
  • #3
Bread18 said:
Try inversing both sides

How would I find the inverse of dv/dt we have never done something like that before.
 
  • #4
I know that I need to get it so that dv and v are on the same side
Take the kv term over to the other side. Multiply both sides by dt. Integrate.
You will need to remember that the integral of v*dt is distance. It works out nicely this way. I don't understand the inverse method.
 
  • #5
You inverse both sides to get dt/dv = m/(-mg - kv) and then multiply both sides by dv
 

1. How do you calculate velocity as a function of time?

The equation for calculating velocity as a function of time is v(t) = s/t, where v is the velocity, s is the displacement, and t is the time.

2. What is the difference between average velocity and instantaneous velocity?

Average velocity is the total displacement divided by the total time, while instantaneous velocity is the velocity at a specific moment in time.

3. How do you find the instantaneous velocity from a position vs. time graph?

The instantaneous velocity at a specific time can be found by finding the slope of the tangent line to the curve on the position vs. time graph at that time.

4. What units are used to measure velocity?

Velocity is typically measured in meters per second (m/s) or kilometers per hour (km/h). However, other units such as feet per second (ft/s) or miles per hour (mph) may also be used.

5. How does acceleration affect velocity as a function of time?

Acceleration is the rate of change of velocity over time. If acceleration is constant, velocity as a function of time can be determined using the equation v(t) = v0 + at, where v0 is the initial velocity and a is the acceleration.

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