If body having initial velocity zero is moving with uniform acceleration `8m//sec^(2)` the distance travelled by it in fifth second will be

Options

A. 1.25 m
B. 2.25 m
C. 6.25 m
D. 36m

Answer

To solve the problem of finding the distance traveled by a body in the fifth second when it starts from rest and accelerates uniformly, we can use the formula for the distance covered in the nth second of motion:

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Initial velocity (u) = 0 m/s (the body starts from rest)
- Acceleration (a) = 8 m/s²
- We want to find the distance traveled in the nth second where n = 5.

2. **Use the Formula for Distance in nth Second:**
The formula for the distance traveled in the nth second is given by:
\[ S_n = u + \frac{1}{2} a (2n - 1) \]
where:
- \( S_n \) = distance traveled in the nth second
- \( u \) = initial velocity
- \( a \) = acceleration
- \( n \) = the specific second we are interested in

3. **Substitute the Known Values into the Formula:**
Since \( u = 0 \) and \( a = 8 \) m/s², we can substitute these values into the formula:
\[ S_5 = 0 + \frac{1}{2} \times 8 \times (2 \times 5 - 1) \]

4. **Calculate the Value Inside the Parentheses:**
\[ 2 \times 5 - 1 = 10 - 1 = 9 \]

5. **Calculate the Distance:**
Now substitute back into the equation:
\[ S_5 = \frac{1}{2} \times 8 \times 9 \]
\[ S_5 = 4 \times 9 = 36 \text{ meters} \]

6. **Conclusion:**
The distance traveled by the body in the fifth second is **36 meters**.

### Final Answer:
The distance traveled by the body in the fifth second is **36 meters**.

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