The position 'x' of a particle moving along x-axis at any instant t represent by given equation
`t= sqrtx+3,` where x is in M , where x is in meters and t is in seconds. The position of particle at the instant when its velocity is zero.

Options

A. Zero
B. 12 m
C. 18 m
D. 6 m

Explanation

To find the position of the particle at the instant when its velocity is zero, we will follow these steps:

### Step 1: Rearranging the given equation
The position of the particle is given by the equation:
\[ t = \sqrt{x} + 3 \]

To express \( x \) in terms of \( t \), we rearrange the equation:
\[ \sqrt{x} = t - 3 \]

### Step 2: Squaring both sides
Next, we square both sides to eliminate the square root:
\[ x = (t - 3)^2 \]

### Step 3: Finding the velocity
The velocity \( v \) of the particle is given by the derivative of position \( x \) with respect to time \( t \):
\[ v = \frac{dx}{dt} \]

Differentiating \( x = (t - 3)^2 \) with respect to \( t \):
\[ \frac{dx}{dt} = 2(t - 3) \]

### Step 4: Setting the velocity to zero
To find the instant when the velocity is zero, we set the expression for velocity equal to zero:
\[ 2(t - 3) = 0 \]

### Step 5: Solving for \( t \)
Solving the equation:
\[ t - 3 = 0 \]
\[ t = 3 \text{ seconds} \]

### Step 6: Finding the position at \( t = 3 \)
Now, we substitute \( t = 3 \) back into the equation for \( x \):
\[ x = (3 - 3)^2 \]
\[ x = 0^2 \]
\[ x = 0 \text{ meters} \]

### Conclusion
The position of the particle at the instant when its velocity is zero is:
\[ \boxed{0 \text{ meters}} \]

---