An object falling through a fluid is observed to have acceleration given by ` a= g- bv` where ` g= gravitational acceleration and (b) is constant. After a long time of rlease. It is observed to fall with constant speed. What must be the value of constant speed ?

Options

A. g/b
B. b/g
C. bg
D. b

Explanation

To solve the problem step by step, we will analyze the given information and apply the relevant physics concepts.

### Step 1: Understand the equation of motion
The acceleration of the object falling through a fluid is given by the equation:
\[ a = g - bv \]
where:
- \( a \) is the acceleration,
- \( g \) is the gravitational acceleration,
- \( b \) is a constant,
- \( v \) is the velocity of the object.

### Step 2: Identify the condition for constant speed
When an object falls with a constant speed, its acceleration becomes zero. This is because constant speed means there is no change in velocity over time.

### Step 3: Set acceleration to zero
Since we are looking for the condition when the object reaches constant speed, we set the acceleration \( a \) to zero:
\[ 0 = g - bv \]

### Step 4: Rearrange the equation
Now, we can rearrange the equation to solve for \( v \):
\[ bv = g \]

### Step 5: Solve for constant speed \( v \)
To isolate \( v \), divide both sides of the equation by \( b \):
\[ v = \frac{g}{b} \]

### Conclusion
The value of the constant speed \( v \) that the object falls with after a long time is:
\[ v = \frac{g}{b} \]