Calculating the Total Distance Traveled

Oct 13, 2025 by talynt.org 39 views

Understanding the Problem

To solve this problem, we need to understand the concept of speed and how it relates to distance and time. Speed is defined as the distance traveled per unit time. In this case, we are given the distance traveled by the train (300 meters) and the time taken to travel that distance (50 seconds). We need to find the speed of the train in kilometers per hour.

Calculating the Total Distance Traveled

The train crosses a platform that is thrice its length, which means the platform is 3 x 300 = 900 meters long. Since the train crosses the platform thrice, it travels a total distance of 300 + 900 + 900 = 2100 meters.

Converting Time from Seconds to Hours

To find the speed in kilometers per hour, we need to convert the time from seconds to hours. There are 3600 seconds in an hour, so we can convert 50 seconds to hours as follows:

50 seconds / 3600 seconds/hour = 0.0139 hours

Calculating the Speed of the Train

Now that we have the total distance traveled (2100 meters) and the time taken to travel that distance (0.0139 hours), we can calculate the speed of the train as follows:

Speed = Distance / Time = 2100 meters / 0.0139 hours = 150,711 meters/hour

Converting Speed from Meters per Hour to Kilometers per Hour

To convert the speed from meters per hour to kilometers per hour, we can divide the speed by 1000 (since there are 1000 meters in a kilometer):

Speed = 150,711 meters/hour / 1000 = 150.711 kilometers/hour

Conclusion

Therefore, the speed of the train is approximately 150.711 kilometers per hour.

Additional Information

It's worth noting that the speed of the train can also be calculated using the formula:

Speed = Distance / Time

However, in this case, we need to use the total distance traveled (2100 meters) and the time taken to travel that distance (0.0139 hours). We can also use the formula:

Speed = (Distance / Time) x (3600 / 1000)

This formula takes into account the conversion from seconds to hours and meters to kilometers.

Real-World Applications

Understanding the concept of speed and how to calculate it is crucial in various real-world applications, such as:

Transportation: Calculating the speed of vehicles is essential for determining travel times, fuel efficiency, and safety.
Aerodynamics: Understanding the speed of objects in flight is critical for designing aircraft and predicting air resistance.
Physics: Calculating speed is a fundamental concept in physics, and it has numerous applications in fields such as mechanics, thermodynamics, and electromagnetism.

Final Thoughts

In conclusion, the speed of the train is approximately 150.711 kilometers per hour. This problem demonstrates the importance of understanding the concept of speed and how to calculate it using the formula: Speed = Distance / Time. The real-world applications of this concept are vast and varied, and it is essential to have a solid understanding of speed in various fields.

Understanding the Problem

Calculating the Total Distance Traveled

Converting Time from Seconds to Hours

To find the speed in kilometers per hour, we need to convert the time from seconds to hours. There are 3600 seconds in an hour, so we can convert 50 seconds to hours as follows:

50 seconds / 3600 seconds/hour = 0.0139 hours

Calculating the Speed of the Train

Now that we have the total distance traveled (2100 meters) and the time taken to travel that distance (0.0139 hours), we can calculate the speed of the train as follows:

Speed = Distance / Time = 2100 meters / 0.0139 hours = 150,711 meters/hour

Converting Speed from Meters per Hour to Kilometers per Hour

To convert the speed from meters per hour to kilometers per hour, we can divide the speed by 1000 (since there are 1000 meters in a kilometer):

Speed = 150,711 meters/hour / 1000 = 150.711 kilometers/hour

Conclusion

Therefore, the speed of the train is approximately 150.711 kilometers per hour.

Additional Information

It's worth noting that the speed of the train can also be calculated using the formula:

Speed = Distance / Time

However, in this case, we need to use the total distance traveled (2100 meters) and the time taken to travel that distance (0.0139 hours). We can also use the formula:

Speed = (Distance / Time) x (3600 / 1000)

This formula takes into account the conversion from seconds to hours and meters to kilometers.

Real-World Applications

Understanding the concept of speed and how to calculate it is crucial in various real-world applications, such as:

Transportation: Calculating the speed of vehicles is essential for determining travel times, fuel efficiency, and safety.
Aerodynamics: Understanding the speed of objects in flight is critical for designing aircraft and predicting air resistance.
Physics: Calculating speed is a fundamental concept in physics, and it has numerous applications in fields such as mechanics, thermodynamics, and electromagnetism.

Final Thoughts

Q: What is the total distance traveled by the train?

A: The total distance traveled by the train is 2100 meters, which is the sum of the length of the train (300 meters) and the length of the platform (900 meters) thrice.

Q: How do we convert 50 seconds to hours?

A: To convert 50 seconds to hours, we divide 50 by 3600 (since there are 3600 seconds in an hour). This gives us 0.0139 hours.

Q: What is the formula for calculating the speed of the train?

A: The formula for calculating the speed of the train is Speed = Distance / Time.

Q: How do we convert the speed from meters per hour to kilometers per hour?

A: To convert the speed from meters per hour to kilometers per hour, we divide the speed by 1000 (since there are 1000 meters in a kilometer).

Q: What are some real-world applications of the concept of speed?

A: Some real-world applications of the concept of speed include transportation, aerodynamics, and physics.

Q: Why is it essential to have a solid understanding of speed in various fields?

A: It is essential to have a solid understanding of speed in various fields because it has numerous applications in fields such as mechanics, thermodynamics, and electromagnetism.

Q: Can you provide an example of how to calculate the speed of the train using the formula Speed = (Distance / Time) x (3600 / 1000)?

A: Yes, the formula can be used as follows:

Speed = (2100 meters / 0.0139 hours) x (3600 / 1000) = 150,711 meters/hour = 150.711 kilometers/hour

Q: What is the speed of the train in km/hr?

A: The speed of the train is approximately 150.711 kilometers per hour.