The displacement of a body along X-axis depends on time as `sqrt(x)=t+1`. Then the velocity of body.

Options

A. increases with time
B. decreases with time
C. independent of time
D. None of these

Explanation

To solve the problem, we need to find the velocity of a body whose displacement along the X-axis is given by the equation \( \sqrt{x} = t + 1 \).

### Step-by-Step Solution:

1. **Start with the given equation:**
\[ \sqrt{x} = t + 1 \]

2. **Square both sides to eliminate the square root:**
\[ x = (t + 1)^2 \]

3. **Expand the right-hand side:**
\[ x = t^2 + 2t + 1 \]

4. **Differentiate \( x \) with respect to \( t \) to find the velocity \( v \):**
\[ v = \frac{dx}{dt} \]

5. **Differentiate the expression \( x = t^2 + 2t + 1 \):**
- The derivative of \( t^2 \) is \( 2t \).
- The derivative of \( 2t \) is \( 2 \).
- The derivative of a constant (1) is \( 0 \).

Therefore,
\[ \frac{dx}{dt} = 2t + 2 \]

6. **Thus, the velocity of the body is:**
\[ v = 2t + 2 \]

### Final Answer:
The velocity of the body as a function of time is:
\[ v(t) = 2t + 2 \]