Calculating the Speed of a Train: A Real-World Example

In the realm of physics, understanding the motion and speed of trains can be both practical and theoretical. Consider a scenario where a 225-meter train crosses another 150-meter train in 12.5 seconds. If the first train is traveling at a speed of 72 kilometers per hour (km/h), what is the speed of the second train? Let's break down the solution step by step to understand how to approach such a problem.

Step 1: Convert Speed to m/s

First, we need to convert the speed of the 72 km/h train into meters per second (m/s).

Speed (m/s) Speed (km/h) × (1000 m / 3600 s)

Speed (m/s) 72 × (1000 / 3600) 20 m/s

Step 2: Calculate the Total Distance Covered

The total distance covered when the two trains cross each other is the sum of their lengths.

Total distance 225 meters 150 meters 375 meters

Step 3: Use the Formula for Relative Speed

Using the formula for relative speed, which is the speed at which one train appears to move relative to the other when they are moving in opposite directions, we can calculate the relative speed.

Relative speed Total distance / Time

Relative speed 375 meters / 12.5 seconds 30 m/s

Step 4: Calculate the Speed of the Other Train

Now that we have the relative speed, we can calculate the speed of the second train.

If the speed of the first train is 20 m/s and the relative speed is 30 m/s, then:

30 m/s 20 m/s x (speed of the other train)

x 30 m/s - 20 m/s 10 m/s

Converting back to km/h, we get:

Speed (km/h) 10 m/s × (3600 s / 1000 m) 36 km/h

Thus, the speed of the other train is 36 km/h.

Conclusion

By applying the principles of physics and basic arithmetic, we can calculate the speed of the second train in this scenario. This example demonstrates the importance of converting units and using the appropriate formulas when solving real-world physics problems.

Additional Information

Total length: The total length of the trains is 225 meters 150 meters 375 meters.

Time: The time taken for the trains to cross each other is 12.5 seconds.

Speed of one train: 72 km/h 20 m/s.

Speed of another train: 10 m/s (or 36 km/h).

Frequently Asked Questions

Q: What is relative speed?
Relative speed is the speed at which one object appears to move relative to another when they are moving relative to each other.

Q: Why is it important to convert units in physics problems?
Accuracy and consistency in units are crucial for obtaining correct results in physics problems. Incorrect unit conversions can lead to significant errors in your calculations.

Q: How do you calculate the speed of two objects moving in the same direction?
When two objects are moving in the same direction, you subtract the speed of the slower object from the speed of the faster object to find the relative speed.