A constant force acts on a particle and its displacement x (in cm) is related to the time t (in s) by the equation `t=sqrtx +3`, when the velocity of the particle is zero, its displacement ( in cm) is

Options

A. Zero
B. 1
C. 2
D. 3

Answer

To solve the problem step by step, we will follow the reasoning provided in the video transcript.

### Step 1: Understand the given equation
The relationship between displacement \( x \) (in cm) and time \( t \) (in seconds) is given by the equation:
\[ t = \sqrt{x} + 3 \]

### Step 2: Rearrange the equation to express \( x \) in terms of \( t \)
To find \( x \) in terms of \( t \), we can rearrange the equation:
\[ \sqrt{x} = t - 3 \]
Now, squaring both sides gives:
\[ x = (t - 3)^2 \]

### Step 3: Differentiate to find velocity
Velocity \( v \) is defined as the rate of change of displacement with respect to time, which can be expressed as:
\[ v = \frac{dx}{dt} \]
Now, we differentiate \( x = (t - 3)^2 \):
\[ \frac{dx}{dt} = 2(t - 3) \cdot \frac{d(t - 3)}{dt} \]
Since \( \frac{d(t - 3)}{dt} = 1 \), we have:
\[ v = 2(t - 3) \]

### Step 4: Set velocity to zero to find the time
To find the time when the velocity is zero, we set \( v = 0 \):
\[ 2(t - 3) = 0 \]
This simplifies to:
\[ t - 3 = 0 \implies t = 3 \text{ seconds} \]

### Step 5: Find displacement at \( t = 3 \)
Now we substitute \( t = 3 \) back into the equation for \( x \):
\[ x = (3 - 3)^2 = 0^2 = 0 \text{ cm} \]

### Conclusion
Thus, when the velocity of the particle is zero, its displacement is:
\[ \boxed{0 \text{ cm}} \]

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