The displacement 'x' (in meter) of a particle of mass 'm' (in kg) moving in one dimension under the action of a force is released to time 't' (in sec) by `t = sqrt(x) + 3`. The displacement of the particle when its velocity is zero will be.

Options

A. 2 m
B. 4 m
C. zero
D. 6 m

Explanation

To solve the problem, we need to find the displacement \( x \) of a particle when its velocity is zero. The relationship between time \( t \) and displacement \( x \) is given by the equation:

\[ t = \sqrt{x} + 3 \]

### Step 1: Rearranging the equation
First, we can rearrange the equation to express \( x \) in terms of \( t \):

\[ t - 3 = \sqrt{x} \]

Now, squaring both sides gives us:

\[ (t - 3)^2 = x \]

### Step 2: Finding the velocity
To find the velocity, we differentiate \( x \) with respect to \( t \):

\[ \frac{dx}{dt} = 2(t - 3) \]

### Step 3: Setting the velocity to zero
We need to find the time \( t \) when the velocity is zero:

\[ 2(t - 3) = 0 \]

Dividing both sides by 2:

\[ t - 3 = 0 \]

Thus, we find:

\[ t = 3 \text{ seconds} \]

### Step 4: Finding displacement at \( t = 3 \)
Now, we substitute \( t = 3 \) back into the equation for \( x \):

\[ x = (3 - 3)^2 = 0^2 = 0 \]

### Conclusion
Therefore, the displacement of the particle when its velocity is zero is:

\[ \boxed{0 \text{ meters}} \]