The distance travelled by a particle starting from rest and moving with an acceleration `(4)/(3) ms^-2`, in the third second is.

Options

A. 6 m
B. 4 m
C. `(10)/(3) m`
D. `(19)/(3) m`

Explanation

To find the distance travelled by a particle starting from rest and moving with an acceleration of \( \frac{4}{3} \, \text{m/s}^2 \) in the third second, we can use the formula for the distance travelled in the nth second:

\[ s_n = u + \frac{1}{2} a (2n - 1) \]

Where:
- \( s_n \) is the distance travelled in the nth second,
- \( u \) is the initial velocity,
- \( a \) is the acceleration,
- \( n \) is the second for which we want to find the distance.

### Step-by-Step Solution:

1. **Identify the given values:**
- Initial velocity \( u = 0 \, \text{m/s} \) (since the particle starts from rest).
- Acceleration \( a = \frac{4}{3} \, \text{m/s}^2 \).
- We want to find the distance travelled in the third second, so \( n = 3 \).

2. **Substitute the values into the formula:**
\[ s_3 = u + \frac{1}{2} a (2n - 1) \]
Substituting the known values:
\[ s_3 = 0 + \frac{1}{2} \left(\frac{4}{3}\right) (2 \times 3 - 1) \]

3. **Calculate \( 2n - 1 \):**
\[ 2n - 1 = 2 \times 3 - 1 = 6 - 1 = 5 \]

4. **Substitute this back into the equation:**
\[ s_3 = \frac{1}{2} \left(\frac{4}{3}\right) \times 5 \]

5. **Calculate \( \frac{1}{2} \times \frac{4}{3} \):**
\[ \frac{1}{2} \times \frac{4}{3} = \frac{4}{6} = \frac{2}{3} \]

6. **Now multiply by 5:**
\[ s_3 = \frac{2}{3} \times 5 = \frac{10}{3} \, \text{m} \]

7. **Final result:**
The distance travelled by the particle in the third second is \( \frac{10}{3} \, \text{m} \).

### Summary:
The distance travelled by the particle in the third second is \( \frac{10}{3} \, \text{m} \).