Question

A Train, going at speed of 72 km/h, passes a station (160 meter long) in 18 second. In how much time the train can Cross a man standing on the station?

Hint:

Always ensure that all units are consistent (meters with seconds, kilometers with hours) before applying the speed-distance-time formulas. The conversion factor for km/h to m/s is 5/18.

Answer 1

Correct Answer: 10

Step 1: Understanding the Question:
First, we need to find the length of the train using the information about it passing a station. Then, we use the train's length and speed to find the time it takes to pass a stationary man.
Step 2: Key Formula or Approach:
- Convert speed from km/h to m/s: Speed (m/s) = Speed (km/h) \(\times \frac{5}{18}\).
- When a train crosses a platform/station, the total distance covered is (Length of Train + Length of Platform).
- When a train crosses a stationary man (point object), the distance covered is the Length of the Train.
- Time = Distance / Speed.
Step 3: Detailed Explanation:
Part 1: Find the length of the train
Speed of the train = 72 km/h.
Speed in m/s = \(72 \times \frac{5}{18} = 4 \times 5 = 20\) m/s.
Length of the station = 160 m.
Time taken to pass the station = 18 seconds.
Total distance covered = Speed \(\times\) Time = 20 \(\times\) 18 = 360 meters.
We know, Total distance = Length of Train (L\(_t\)) + Length of Station.
360 = L\(_t\) + 160.
L\(_t\) = 360 - 160 = 200 meters.
Part 2: Find the time to cross a man
Now the train has to cross a standing man.
Distance to be covered = Length of Train = 200 meters.
Speed of the train = 20 m/s.
Time taken = Distance / Speed = 200 / 20 = 10 seconds.
Step 4: Final Answer:
The train can cross the man in 10 seconds.