Particle is moving in a straight line. Distance x is related to the time t by the equation `t=sqrt(x)+3`. Distance x is measured in metres and time t is seconds. After how many seconds will the particle come to the rest?

Explanation

To solve the problem, we need to find out when the particle comes to rest, which means we need to determine when its velocity becomes zero. The relationship between distance \( x \) and time \( t \) is given by the equation:

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

### Step-by-Step Solution:

1. **Rearranging the Equation**:
Start by isolating \( x \) in terms of \( t \):
\[ t - 3 = \sqrt{x} \]
Now, square both sides to eliminate the square root:
\[ (t - 3)^2 = x \]

2. **Expanding the Equation**:
Expand the squared term:
\[ x = t^2 - 6t + 9 \]
This gives us the equation for distance \( x \) as a function of time \( t \).

3. **Finding Velocity**:
The velocity \( v \) is defined as the derivative of distance with respect to time:
\[ v = \frac{dx}{dt} \]
Differentiate the expression for \( x \):
\[ v = \frac{d}{dt}(t^2 - 6t + 9) \]
Applying the power rule:
\[ v = 2t - 6 \]

4. **Setting Velocity to Zero**:
To find when the particle comes to rest, set the velocity \( v \) to zero:
\[ 0 = 2t - 6 \]

5. **Solving for Time \( t \)**:
Rearranging the equation gives:
\[ 2t = 6 \]
Dividing both sides by 2:
\[ t = 3 \text{ seconds} \]

### Conclusion:
The particle will come to rest after **3 seconds**.