Solving dv/dt = Bv - Av² for initial acceleration and terminal velocity

[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 acceleration becomes 0, you set the whole equation to 0.
0=Bv - Av²