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 1: Rearranging the equation
We start with the given equation:
\[ \sqrt{x} = t + 1 \]
To eliminate the square root, we square both sides:
\[ x = (t + 1)^2 \]

### Step 2: Expanding the equation
Now we expand the right-hand side:
\[ x = t^2 + 2t + 1 \]

### Step 3: Finding the velocity
The velocity \( v \) is defined as the derivative of displacement \( x \) with respect to time \( t \):
\[ v = \frac{dx}{dt} \]
We differentiate \( x = t^2 + 2t + 1 \):
\[ \frac{dx}{dt} = \frac{d}{dt}(t^2 + 2t + 1) \]
Using the power rule of differentiation:
\[ \frac{dx}{dt} = 2t + 2 \]

### Step 4: Analyzing the velocity
The expression for velocity we found is:
\[ v = 2t + 2 \]
This shows that as time \( t \) increases, the velocity \( v \) also increases since it is a linear function of \( t \).

### Conclusion
Thus, the velocity of the body increases with time.