Answered

Welcome to Westonci.ca, the ultimate question and answer platform. Get expert answers to your questions quickly and accurately. Our platform provides a seamless experience for finding precise answers from a network of experienced professionals. Join our platform to connect with experts ready to provide precise answers to your questions in different areas.

A tourist cab goes from Delhi to Agra in the morning and covers the distance of [tex]240 \, \text{km}[/tex] in 4.5 hours. The cab returns from Agra to Delhi during the night, covering the journey in 3.5 hours.

Calculate the average speed and average velocity.

---

Note: Here are the steps for the calculation:

1. Average Speed:
- Total Distance = Distance from Delhi to Agra + Distance from Agra to Delhi
- Total Time = Time taken from Delhi to Agra + Time taken from Agra to Delhi
- Average Speed = Total Distance / Total Time

2. Average Velocity:
- Since the cab returns to the starting point, the displacement is zero.
- Average Velocity = Total Displacement / Total Time

In this scenario, the average velocity would be zero because the displacement is zero.

Sagot :

GinnyAnswer
To solve this problem, we'll break it down step by step and then provide a detailed explanation to find the average speed and average velocity of the cab.

### Given Data:
1. Distance from Delhi to Agra: [tex]\(240 \text{ km}\)[/tex]
2. Time taken to travel from Delhi to Agra in the morning: [tex]\(45 \text{ hours}\)[/tex]
3. Time taken to return from Agra to Delhi during the night: [tex]\(3.5 \text{ hours}\)[/tex]

### Step-by-Step Solution:

#### 1. Calculate the Total Distance:
Since the cab travels from Delhi to Agra and back from Agra to Delhi, the total distance covered is the sum of both the trips.

[tex]\[ \text{Total Distance} = \text{Distance from Delhi to Agra} + \text{Distance from Agra to Delhi} = 240 \text{ km} + 240 \text{ km} = 480 \text{ km} \][/tex]

#### 2. Calculate the Total Time:
The total time for the round trip is the sum of the time taken for both legs of the journey.

[tex]\[ \text{Total Time} = \text{Time taken from Delhi to Agra} + \text{Time taken from Agra to Delhi} = 45 \text{ hours} + 3.5 \text{ hours} = 48.5 \text{ hours} \][/tex]

#### 3. Calculate the Average Speed:
The average speed is the total distance covered divided by the total time taken.

[tex]\[ \text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} = \frac{480 \text{ km}}{48.5 \text{ hours}} \approx 9.897 \text{ km/h} \][/tex]

#### 4. Calculate the Average Velocity:
Average velocity is defined as the total displacement divided by the total time taken. Displacement is the straight-line distance between the initial and final positions.

Since the cab returns to the original starting point (Delhi), the total displacement is zero.

[tex]\[ \text{Total Displacement} = \text{Final Position} - \text{Initial Position} = 0 \text{ km} \][/tex]

[tex]\[ \text{Average Velocity} = \frac{\text{Total Displacement}}{\text{Total Time}} = \frac{0 \text{ km}}{48.5 \text{ hours}} = 0 \text{ km/h} \][/tex]

### Conclusion:
- The total distance covered during the round trip is [tex]\(480 \text{ km}\)[/tex].
- The total time taken for the round trip is [tex]\(48.5 \text{ hours}\)[/tex].
- The average speed of the cab is approximately [tex]\(9.897 \text{ km/h}\)[/tex].
- The average velocity of the cab is [tex]\(0 \text{ km/h}\)[/tex].

These results have been derived from the given data and provide a complete and precise solution to the problem.
Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Westonci.ca is committed to providing accurate answers. Come back soon for more trustworthy information.