Need help on Motion in a Resistive Medium

[eyvhgi557r]

1. The motion of a body falling from rest in a resistive medium is dv/dt = Bv - Av^2.


2. Find it's initial acceleration.
Find the velocity at which the acceleration becomes zero.


3. B and A are constants.

dv/dt = acceleration = Bv - Av^2.

vf = vi + at
vf = 0 + Bv - Av^2(t)
vf = Bv - Av^2(t)

Where am I going with this?

 

[southernbelle]

dv/dt is acceleration.

a. So, when it says find the initial acceleration you just set v=0.
a= B(0) - A(0)²


b. To find the velocity at which accleration becomes 0, you set the whole equation to 0.
0=Bv - Av²

 

[baba89]

I can provide some insights and guidance on this topic. First, let's break down the equation provided: dv/dt = Bv - Av^2. This is a differential equation that describes the motion of a body falling in a resistive medium. The left side represents the acceleration, while the right side represents the forces acting on the body - the resistive force (Bv) and the drag force (Av^2).

To answer the first question, we can find the initial acceleration by setting v = 0, since the body is falling from rest. This gives us a = -Av^2, which means the acceleration is dependent on the square of the velocity and is always negative. This makes sense as the resistive and drag forces act to slow down the body's motion.

Next, we can find the velocity at which the acceleration becomes zero by setting a = 0. This gives us Bv - Av^2 = 0, which can be rearranged to v = B/A. This is the terminal velocity, which is the maximum velocity that the body can reach in the resistive medium. Beyond this velocity, the drag force becomes equal to the resistive force and the net acceleration becomes zero.

Finally, the constants B and A can be determined experimentally by observing the motion of the body in the resistive medium. By measuring the initial acceleration and terminal velocity, we can solve for these constants and get a better understanding of the resistive medium's properties.

I hope this helps in your understanding of motion in a resistive medium. Remember, as a scientist, it's important to always question and explore the world around us to gain a deeper understanding of natural phenomena.