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A train 150 m long is running with a speed of 68 kmph. In what time will it pass a man who is running at 8 kmph in the same direction in which the train is going?
The train will pass the man in 0.15 minutes or 9 seconds.
To solve this problem, we need to find the time it takes for the train to pass the man who is running in the same direction.
First, let’s convert the speeds to the same unit. Since the speed of the train is given in km/h, let’s convert the length of the train to kilometers and the speed of the man to km/h:
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Length of the train = 150 meters = 0.15 kilometers (since 1 kilometer = 1000 meters) Speed of the train = 68 km/h Speed of the man = 8 km/h
Now, the relative speed of the train with respect to the man is the difference between their speeds:
Relative speed = Speed of the train – Speed of the man = 68 km/h – 8 km/h = 60 km/h
Now, we can use the formula for time:
Time = Distance / Speed
Since the train needs to cover the length of the man while overtaking him, the distance is equal to the length of the train. Thus:
Time = Length of the train / Relative speed = 0.15 km / 60 km/h = 0.0025 hours
To convert hours to minutes, multiply by 60:
Time = 0.0025 hours * 60 minutes/hour = 0.15 minutes
So, the train will pass the man in 0.15 minutes or 9 seconds.
Speed, Distance and Time
Speed, distance, and time are fundamental concepts in physics and everyday life. They are interrelated through simple equations that help calculate one quantity when the other two are known.
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Speed: Speed is the rate at which an object covers distance. It’s defined as the distance traveled per unit of time. The standard unit of speed in the International System of Units (SI) is meters per second (m/s), although other units like kilometers per hour (km/h) or miles per hour (mph) are commonly used.
Speed = Distance / Time
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Distance: Distance is the total length of the path traveled by an object. It is measured in units such as meters (m), kilometers (km), miles (mi), etc.
Distance = Speed × Time
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Time: Time is the duration or period during which an event occurs or an object is in motion. It’s typically measured in units such as seconds (s), minutes (min), hours (h), etc.
Time = Distance / Speed
These formulas are straightforward to use. For example, if you know the speed of an object and the time it traveled at that speed, you can find out the distance it covered by using the formula “Distance = Speed × Time”. Similarly, if you know the distance traveled and the time taken, you can calculate the speed using “Speed = Distance / Time”. And if you know the distance and speed, you can find out the time taken by using “Time = Distance / Speed”.
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Categories: Math
