For a particle displacement time relation is `t = sqrt(x) + 3`. Its displacement when its velocity is zero -

Options

A. 2m
B. 4m
C. 0
D. None of these

Explanation

To solve the problem, we will follow these steps:

### Step 1: Write the given displacement-time relation
The displacement-time relation is given as:
\[ t = \sqrt{x} + 3 \]

### Step 2: Rearrange the equation to express displacement \( x \) in terms of time \( t \)
We can rearrange the equation to isolate \( \sqrt{x} \):
\[ \sqrt{x} = t - 3 \]

Now, squaring both sides to solve for \( x \):
\[ x = (t - 3)^2 \]

### Step 3: Differentiate \( x \) with respect to \( t \) to find the velocity
The velocity \( v \) is defined as the derivative of displacement \( x \) with respect to time \( t \):
\[ v = \frac{dx}{dt} \]

Differentiating \( x = (t - 3)^2 \):
\[ v = \frac{d}{dt}((t - 3)^2) \]
Using the chain rule:
\[ v = 2(t - 3) \cdot \frac{d}{dt}(t - 3) = 2(t - 3) \cdot 1 = 2(t - 3) \]

### Step 4: Set the velocity \( v \) to zero to find the time \( t \)
To find when the velocity is zero:
\[ 2(t - 3) = 0 \]

Solving for \( t \):
\[ t - 3 = 0 \]
\[ t = 3 \]

### Step 5: Substitute \( t = 3 \) back into the displacement equation to find \( x \)
Now we will substitute \( t = 3 \) back into the equation for \( x \):
\[ x = (3 - 3)^2 \]
\[ x = 0^2 \]
\[ x = 0 \]

### Final Answer
The displacement when the velocity is zero is:
\[ \boxed{0} \]

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