The displacement of a body along z-axis depends on time as `sqrt(x)=3t+5` . Then the velocity of body :

Options

A. Increase with time
B. Independent of time
C. Decrease with time
D. None of these

Explanation

To find the velocity of the body given the displacement along the z-axis as \( \sqrt{x} = 3t + 5 \), we can follow these steps:

### Step 1: Square Both Sides
Given the equation:
\[ \sqrt{x} = 3t + 5 \]
we square both sides to eliminate the square root:
\[ x = (3t + 5)^2 \]

### Step 2: Expand the Right Side
Now, we expand the right side:
\[ x = (3t + 5)(3t + 5) = 9t^2 + 30t + 25 \]

### Step 3: Differentiate with Respect to Time
To find the velocity, we need to differentiate \( x \) with respect to \( t \):
\[ v = \frac{dx}{dt} = \frac{d}{dt}(9t^2 + 30t + 25) \]
Using the power rule of differentiation:
\[ v = 18t + 30 \]

### Step 4: Analyze the Velocity
The expression for velocity \( v = 18t + 30 \) shows that the velocity is a linear function of time. As time increases, the velocity also increases.

### Conclusion
Thus, the velocity of the body is given by:
\[ v = 18t + 30 \]