Understanding Train Speed and Tunnel Crossing

This problem asks us to find the speed of a train given its length, the length of a tunnel it passes through, and the time taken for the crossing. When a train passes a tunnel, the total distance the train travels to completely clear the tunnel is the sum of the train's length and the tunnel's length.

Calculating Total Distance for Train to Pass Tunnel

To find the total distance the train covers from the moment the front of the train enters the tunnel until the moment the back of the train leaves the tunnel, we add the lengths of the train and the tunnel.

• Length of the train = 725 m
• Length of the tunnel = 235 m

Total distance covered = Length of train + Length of tunnel

\( \text{Total Distance} = 725 \text{ m} + 235 \text{ m} \)

\( \text{Total Distance} = 960 \text{ m} \)

So, the train travels a total distance of 960 meters to pass completely through the tunnel.

Using Time and Distance to Find Speed

We are given the time taken for this process.

• Time taken = 48 seconds

The formula to calculate speed is:

\( \text{Speed} = \frac{\text{Distance}}{\text{Time}} \)

Now, we can calculate the speed of the train in meters per second (m/s).

\( \text{Speed} = \frac{960 \text{ m}}{48 \text{ s}} \)

\( \text{Speed} = 20 \text{ m/s} \)

The speed of the train is 20 meters per second.

Converting Speed from m/s to km/h

The options for the answer are given in kilometers per hour (km/h). We need to convert the speed from m/s to km/h.

To convert a speed from meters per second (m/s) to kilometers per hour (km/h), we multiply the speed in m/s by the fraction \( \frac{18}{5} \).

\( \text{Speed (km/h)} = \text{Speed (m/s)} \times \frac{18}{5} \)

Let's perform the conversion:

\( \text{Speed (km/h)} = 20 \times \frac{18}{5} \)

\( \text{Speed (km/h)} = (20 \div 5) \times 18 \)

\( \text{Speed (km/h)} = 4 \times 18 \)

\( \text{Speed (km/h)} = 72 \text{ km/h} \)

Final Train Speed Calculation

The speed of the train is 72 km/h.

Comparing this with the given options:

• Option 1: 42 km/h
• Option 2: 72 km/h
• Option 3: 36 km/h
• Option 4: 100 km/h

The calculated speed matches Option 2.

Revision Table: Train Speed Problem

Additional Information: Time, Distance, and Speed Concepts

Understanding the relationship between time, distance, and speed is fundamental in physics and many real-world problems. The basic relationship is:

\( \text{Speed} = \frac{\text{Distance}}{\text{Time}} \)

This formula can be rearranged to find distance or time if the other two quantities are known:

• Distance = Speed \( \times \) Time
• Time = \( \frac{\text{Distance}}{\text{Speed}} \)

It is very important to use consistent units when applying these formulas. If distance is in meters and time is in seconds, speed will be in meters per second. If distance is in kilometers and time is in hours, speed will be in kilometers per hour.

The conversion factor between m/s and km/h comes from:

• 1 km = 1000 meters
• 1 hour = 3600 seconds

So, \( 1 \text{ km/h} = \frac{1 \text{ km}}{1 \text{ hour}} = \frac{1000 \text{ m}}{3600 \text{ s}} = \frac{10}{36} \text{ m/s} = \frac{5}{18} \text{ m/s} \). Conversely, \( 1 \text{ m/s} = \frac{18}{5} \text{ km/h} \).

When a train passes a stationary object of some length (like a tunnel, bridge, or platform), the distance covered by the train is the length of the train plus the length of the object.

When a train passes a point object (like a pole, tree, or a person), the distance covered by the train is just the length of the train itself.