A body starting from rest has an acceleration of `5m//s^(2)`. Calculate the distance travelled by it in `4^(th)` second.

Explanation

To solve the problem of calculating the distance travelled by a body in the 4th second, we can follow these steps:

### Step-by-Step Solution:

1. **Identify Given Data:**
- Initial velocity, \( u = 0 \) (the body starts from rest)
- Acceleration, \( a = 5 \, \text{m/s}^2 \)
- We need to find the distance travelled in the 4th second, which corresponds to \( n = 4 \).

2. **Use the Formula for Distance Travelled in the nth Second:**
The distance travelled in the nth second can be calculated using the formula:
\[ S_n = u + \frac{a}{2} \times (2n - 1) \]
where \( S_n \) is the distance travelled in the nth second.

3. **Substitute the Values into the Formula:**
- Substitute \( u = 0 \), \( a = 5 \, \text{m/s}^2 \), and \( n = 4 \) into the formula:
\[ S_4 = 0 + \frac{5}{2} \times (2 \times 4 - 1) \]

4. **Calculate the Expression Inside the Parentheses:**
- Calculate \( 2 \times 4 - 1 = 8 - 1 = 7 \).

5. **Complete the Calculation:**
- Now substitute back into the equation:
\[ S_4 = \frac{5}{2} \times 7 \]
- This simplifies to:
\[ S_4 = \frac{35}{2} = 17.5 \, \text{meters} \]

6. **Final Answer:**
The distance travelled by the body in the 4th second is \( 17.5 \, \text{meters} \).