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. 40m
B. 36m
C. 100m
D. zero

Answer

To solve the problem of finding the distance traveled by a body in the 5th second when it starts from rest with a uniform acceleration of \(8 \, \text{m/s}^2\), we can use the formula for the distance traveled in the nth second, which is given by:

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

Where:
- \(S_n\) = distance traveled in the nth second
- \(u\) = initial velocity
- \(a\) = acceleration
- \(n\) = 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 body starts from rest)
- Acceleration, \(a = 8 \, \text{m/s}^2\)
- We need to find the distance traveled 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 \(2n - 1\)**:
\[ 2 \cdot 5 - 1 = 10 - 1 = 9 \]

4. **Substitute \(2n - 1\) back into the equation**:
\[ S_5 = 0 + 4 \cdot 9 \]

5. **Calculate the final distance**:
\[ S_5 = 36 \, \text{m} \]

Thus, the distance traveled by the body in the 5th second is **36 meters**.