Two trains, 130 m and 110 m long, while going in the same direction, the faster train takes on

step 1 So here we have two trains and the velocity of shorter train is three times the velocity of long

Two trains, 130 m and 110 m long, while going in the same...

Two trains, $130 \mathrm{~m}$ and $110 \mathrm{~m}$ long, while going in the same direction, the faster train takes one minute to pass the other completely. If they are moving in opposite direction, they pass each other completely in 3 seconds. Find the speed of each train (a) $42 \mathrm{~m} / \mathrm{sec}$., $38 \mathrm{~m} / \mathrm{sec}$. (b) $38 \mathrm{~m} / \mathrm{sec}, 36 \mathrm{~m} / \mathrm{sec}$. (c) $36 \mathrm{~m} / \mathrm{sec} ., 42 \mathrm{~m} / \mathrm{sec}$. (d) None of these

Two trains, $130 \mathrm{~m}$ and $110 \mathrm{~m}$ long, while going in the same direction, the faster train takes one minute to pass the other completely. If they are moving in opposite direction, they pass each other completely in 3 seconds. Find the speed of each train
(a) $42 \mathrm{~m} / \mathrm{sec}$., $38 \mathrm{~m} / \mathrm{sec}$. (b) $38 \mathrm{~m} / \mathrm{sec}, 36 \mathrm{~m} / \mathrm{sec}$.
(c) $36 \mathrm{~m} / \mathrm{sec} ., 42 \mathrm{~m} / \mathrm{sec}$.
(d) None of these

Key Concepts

Passing Time in Train Problems

In problems involving trains or other elongated moving objects, the concept of passing time involves the combined lengths of the objects being equal to the relative distance covered during the time it takes one object to completely pass the other. This approach is used to set up equations that relate the speeds of the moving objects with the time it takes for one to overtake or pass the other completely.

Relative Speed

Relative speed is the effective speed at which two objects approach or recede from each other. When two objects move in the same or opposite directions, their relative speeds are calculated by taking the difference or sum of their speeds respectively. This concept is critical in determining how quickly one object will pass another, which is essential in problems involving moving bodies.

Uniform Linear Motion

Uniform linear motion refers to movement at a constant speed along a straight path. This principle ensures that the distance covered is directly proportional to the time spent traveling. It forms the foundation of problems where distance, speed, and time are interrelated and can be manipulated to find unknown quantities.

Distance-Time-Speed Relationship

The relationship between distance, speed, and time, often expressed as distance = speed × time, is fundamental in solving motion problems. By applying this relationship, one can determine how far an object travels given a specific period and speed, or conversely, calculate speed if the distance and time are known.

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