The displacement x of a particle moving in one direction is given by `t=sqrtx +3` , where x in meter and t in sec. What is its displacement when its velocity is zero

Options

A. 3 m/s
B. 2 m/s
C. 1 m/s
D. zero

Answer

To find the displacement \( x \) of a particle when its velocity is zero, we start with the given equation relating displacement \( x \) and time \( t \):

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

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

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

### Step 2: Squaring both sides
Next, we square both sides to eliminate the square root:

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

### Step 3: Finding velocity
To find the velocity, we differentiate \( x \) with respect to \( t \):

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

### Step 4: Setting velocity to zero
We set the velocity \( \frac{dx}{dt} \) to zero to find the time when the velocity is zero:

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

### Step 5: Solving for \( t \)
Solving the equation gives:

\[ t - 3 = 0 \implies t = 3 \text{ seconds} \]

### Step 6: Finding displacement at \( t = 3 \)
Now, we substitute \( t = 3 \) back into the equation for \( x \):

\[ x = (3 - 3)^2 = 0^2 = 0 \text{ meters} \]

### Conclusion
Thus, the displacement when the velocity is zero is:

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

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