A body starting from rest is moving with a uniform acceleration of `8m/s^(2)`. Then the distance travelled by it in 5th second will be

Options

A. 2.00 m
B. 2.56 m
C. 36 m
D. 0.0 m

Answer

To find the distance travelled by a body in the 5th second when it starts from rest and moves with a uniform acceleration of \(8 \, \text{m/s}^2\), we can use the formula for the distance travelled in the nth second:

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

Where:
- \(s_n\) is the distance travelled in the nth second,
- \(u\) is the initial velocity,
- \(a\) is the acceleration,
- \(n\) is the specific second we are interested in.

### Step-by-Step Solution:

1. **Identify the given values**:
- Initial velocity \(u = 0 \, \text{m/s}\) (since the body starts from rest),
- Acceleration \(a = 8 \, \text{m/s}^2\),
- We want to find the distance travelled in the 5th second, so \(n = 5\).

2. **Substitute the values into the formula**:
\[ s_5 = u + \frac{a}{2} \cdot (2n - 1) \]
\[ s_5 = 0 + \frac{8}{2} \cdot (2 \cdot 5 - 1) \]

3. **Calculate \(\frac{a}{2}\)**:
\[ \frac{8}{2} = 4 \]

4. **Calculate \(2n - 1\)**:
\[ 2 \cdot 5 - 1 = 10 - 1 = 9 \]

5. **Combine the results**:
\[ s_5 = 4 \cdot 9 \]

6. **Final calculation**:
\[ s_5 = 36 \, \text{meters} \]

### Conclusion:
The distance travelled by the body in the 5th second is \(36 \, \text{meters}\).