If a train of length 1000 m is cruising at a speed of 90 kmph and crosses a bridge of length 1000 m, what time does it take to completely pass the bridge?
80 s
To solve this problem, we need to calculate the total distance the train must cover to completely pass the bridge and then use the train's speed to find the time taken. It's crucial to ensure all units are consistent before performing calculations.
Train Speed Conversion
The speed of the train is given in kilometers per hour (kmph), while the lengths are in meters. To calculate time in seconds, we must first convert the speed from kmph to meters per second (m/s).
- Given train speed = 90 kmph
- To convert kilometers per hour to meters per second, we multiply the speed by the conversion factor $\frac{5}{18}$.
The conversion is as follows:
$Speed = 90 \text{ kmph} \times \frac{5}{18} \frac{\text{m/s}}{\text{kmph}}$
$Speed = \left(90 \div 18\right) \times 5 \text{ m/s}$
$Speed = 5 \times 5 \text{ m/s}$
$Speed = 25 \text{ m/s}$
| Parameter | Value |
|---|---|
| Initial Train Speed | 90 kmph |
| Converted Train Speed | 25 m/s |
Bridge Crossing Distance
When a train completely crosses a bridge, the total distance it travels is not just the length of the bridge. It must cover its own length in addition to the bridge's length for the entire train to be considered past the bridge.
- Length of the train ($L_{train}$) = 1000 m
- Length of the bridge ($L_{bridge}$) = 1000 m
The total distance (D) required to be covered by the train is:
$Total \text{ Distance } (D) = L_{train} + L_{bridge}$
$Total \text{ Distance } (D) = 1000 \text{ m} + 1000 \text{ m}$
$Total \text{ Distance } (D) = 2000 \text{ m}$
Time Calculation to Cross Bridge
Now that we have the total distance and the train's speed in consistent units, we can calculate the time taken using the fundamental formula: Time = Distance / Speed.
- Total Distance (D) = 2000 m
- Train Speed (V) = 25 m/s
Using the formula, the time (T) taken is:
$Time (T) = \frac{Total \text{ Distance}}{Speed}$
$Time (T) = \frac{2000 \text{ m}}{25 \text{ m/s}}$
$Time (T) = 80 \text{ s}$
| Summary of Values | Calculated Result |
|---|---|
| Train Length | 1000 m |
| Bridge Length | 1000 m |
| Train Speed (m/s) | 25 m/s |
| Total Distance Covered | 2000 m |
| Time Taken to Cross Bridge | 80 s |
Therefore, it takes 80 seconds for the train to completely pass the bridge.
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