Train Speed Calculation How To Find Speed Of Train Passing Through Tunnel

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This article delves into a classic physics problem involving the calculation of a train's speed. We will explore the scenario where a 210-meter long train takes 12 seconds to completely pass through a 90-meter long tunnel. Our goal is to determine the train's speed, providing a step-by-step solution and explanation. This problem is a great example of how to apply basic physics principles to real-world situations.

A train with a length of 210 meters travels through a tunnel that is 90 meters long. The train takes 12 seconds to completely pass through the tunnel. What is the speed of the train?

Before we dive into the calculations, it's important to grasp the underlying concepts. The key here is to understand that the train needs to cover a distance equal to the sum of its own length and the length of the tunnel to completely pass through it. This is because the entire train, from its front to its rear, must exit the tunnel. This problem incorporates the fundamental relationship between distance, speed, and time, which is expressed by the formula:

Speed = Distance / Time

To solve this problem effectively, we need to accurately determine the total distance the train travels and then apply the formula to find its speed. Understanding this concept of relative distances is crucial in solving this type of problem accurately. Let's break down each component to ensure clarity.

Key Concepts Explained

Let’s further explain the key concepts involved in solving this problem:

  1. Distance: The total distance the train covers is not just the length of the tunnel. The train has to travel its own length plus the length of the tunnel to completely clear it. Think of it this way: the front of the train enters the tunnel, and the train is considered to have completely passed through only when the end of the train exits the tunnel. Therefore, the total distance is the sum of the train's length and the tunnel's length.

  2. Time: The time given in the problem is the duration it takes for the entire train to pass through the tunnel. This is the time we will use in our calculation of speed. It’s a straightforward value in this case, but ensuring you understand what this time represents is crucial.

  3. Speed: Speed is the rate at which an object moves, calculated by dividing the distance traveled by the time taken. In this problem, we are trying to find the train's speed, which will be constant throughout its journey through the tunnel. The units of speed will depend on the units of distance and time (e.g., meters per second if distance is in meters and time is in seconds).

Understanding these core concepts will help you approach similar problems with confidence and clarity. Now that we have a firm grasp of these ideas, let’s move on to applying them in our solution.

Now that we understand the concepts, let's solve the problem step-by-step:

  1. Calculate the total distance:

    • Train length = 210 meters
    • Tunnel length = 90 meters
    • Total distance = Train length + Tunnel length = 210 meters + 90 meters = 300 meters

  2. Identify the time taken:

    • Time = 12 seconds

  3. Apply the formula for speed:

    • Speed = Distance / Time
    • Speed = 300 meters / 12 seconds = 25 meters/second

Therefore, the speed of the train is 25 meters per second. This calculation demonstrates the direct application of the speed formula once the total distance and time are correctly identified.

To make this more relatable, let’s convert this speed into kilometers per hour, which is a more commonly used unit in daily life.

Converting to Kilometers Per Hour

To convert the speed from meters per second (m/s) to kilometers per hour (km/h), we use the conversion factor of 3.6. This factor comes from the fact that there are 1000 meters in a kilometer and 3600 seconds in an hour.

The conversion formula is:

Speed (km/h) = Speed (m/s) × 3.6

Applying this to our calculated speed:

Speed = 25 m/s × 3.6 = 90 km/h

So, the speed of the train is 90 kilometers per hour. This conversion gives us a better sense of how fast the train is moving in real-world terms. It’s a practical step that helps in understanding and visualizing the calculated speed.

In conclusion, the speed of the train is 25 meters per second, or 90 kilometers per hour. This problem illustrates a simple yet effective application of physics principles to calculate speed based on distance and time. By carefully considering the total distance the train needs to cover—including its own length and the length of the tunnel—we were able to accurately determine its speed. This example underscores the importance of understanding the relationship between distance, speed, and time, and how these concepts apply in everyday scenarios. Such problems not only enhance our understanding of physics but also improve our analytical and problem-solving skills. Remember, the key to solving these kinds of questions lies in carefully identifying the given information and applying the relevant formulas correctly.

The principles used in this problem are applicable to numerous real-world situations. Understanding how to calculate speed, distance, and time is crucial in various fields such as transportation, logistics, and even sports. For instance, civil engineers use these calculations when designing roads and railways, ensuring safety and efficiency. Similarly, logistics companies rely on these concepts to optimize delivery routes and schedules. In sports, athletes and coaches use speed calculations to assess performance and plan training regimes. Moreover, understanding these concepts is valuable in everyday life, such as when planning travel times or estimating arrival times. The ability to quickly and accurately calculate speed and distance can be a significant advantage in many practical situations. By mastering these fundamental physics concepts, you can gain a better understanding of the world around you and improve your problem-solving skills in various contexts.

To further reinforce your understanding, let's explore some practice problems similar to the one we solved. Working through these examples will help solidify your grasp of the concepts and improve your problem-solving abilities.

Practice Problem 1

A train 150 meters long is running with a speed of 54 km/h. In what time will it pass a bridge 300 meters long?

Solution

  1. First, convert the speed from km/h to m/s: 54 km/h = 54 × (1000/3600) m/s = 15 m/s
  2. Calculate the total distance the train needs to cover: Train length + Bridge length = 150 meters + 300 meters = 450 meters
  3. Use the formula Time = Distance / Speed: Time = 450 meters / 15 m/s = 30 seconds

Therefore, the train will pass the bridge in 30 seconds.

Practice Problem 2

A 200-meter long train crosses a 100-meter long platform in 10 seconds. What is the speed of the train in km/h?

Solution

  1. Calculate the total distance the train needs to cover: Train length + Platform length = 200 meters + 100 meters = 300 meters
  2. Use the formula Speed = Distance / Time: Speed = 300 meters / 10 seconds = 30 m/s
  3. Convert the speed from m/s to km/h: 30 m/s = 30 × 3.6 km/h = 108 km/h

Therefore, the speed of the train is 108 km/h.

Practice Problem 3

A train traveling at 72 km/h passes a stationary pole in 15 seconds. Find the length of the train.

Solution

  1. Convert the speed from km/h to m/s: 72 km/h = 72 × (1000/3600) m/s = 20 m/s
  2. Since the train is passing a stationary pole, the total distance is equal to the length of the train.
  3. Use the formula Distance = Speed × Time: Distance = 20 m/s × 15 seconds = 300 meters

Therefore, the length of the train is 300 meters.

These practice problems illustrate the variations of the same basic concept and formula. Working through these will help you become more comfortable and proficient in solving such problems.