To determine the average speed of a body traveling from point A to point B and then returning from point B to point A, we can follow these steps:
1. Determine the speeds:
- Speed from A to B: [tex]\(25 \text{ m/s}\)[/tex]
- Speed from B to A: [tex]\(50 \text{ m/s}\)[/tex]
2. Assume the distance between A and B:
Let's assume the distance [tex]\(d\)[/tex] is 1 meter (or any other unit, but we'll use 1 meter here for simplicity).
3. Calculate the time taken for each leg of the journey:
- Time taken to travel from A to B:
[tex]\[
\text{Time}_{\text{A to B}} = \frac{d}{\text{Speed}_{\text{A to B}}} = \frac{1 \text{ m}}{25 \text{ m/s}} = 0.04 \text{ s}
\][/tex]
- Time taken to travel from B to A:
[tex]\[
\text{Time}_{\text{B to A}} = \frac{d}{\text{Speed}_{\text{B to A}}} = \frac{1 \text{ m}}{50 \text{ m/s}} = 0.02 \text{ s}
\][/tex]
4. Calculate the total distance traveled:
- Distance from A to B and back to A:
[tex]\[
\text{Total distance} = d + d = 1 \text{ m} + 1 \text{ m} = 2 \text{ m}
\][/tex]
5. Calculate the total time taken:
- Total time for the journey from A to B and back to A:
[tex]\[
\text{Total time} = \text{Time}_{\text{A to B}} + \text{Time}_{\text{B to A}} = 0.04 \text{ s} + 0.02 \text{ s} = 0.06 \text{ s}
\][/tex]
6. Calculate the average speed:
- Average speed is given by the formula:
[tex]\[
\text{Average speed} = \frac{\text{Total distance}}{\text{Total time}} = \frac{2 \text{ m}}{0.06 \text{ s}} = 33.33 \text{ m/s}
\][/tex]
Comparing the given options, the correct answer is:
(d) [tex]\(33.3 \text{ m/s}\)[/tex]
