Introduction- Problems on trains
Problems on trains are simply a part of time and distance chapter frequently asked in many exams.Let’s play with the problems based on train. Train is simply a safer, faster and cheaper mode of transportation. We all have travelled through many trains. A common scenario of crossing a train is observed while sitting on a station bench or window seat.
Ramu is waiting for a train.A train of 50 m passes him at the speed of 36 km/hr. what is the total time taken by the train to cross him?
Answer- Total distance travelled by the train while crossing Ramu = Distance between train head and train tail = Length of train
D = 50 m
V= 36 km/hr = 10 m/sec
T= (D/V)= 5 sec
When a train passes an object with certain length ( O ) , the distance travelled will not be equal to the length of train in this case.
Distance travelled = Length of train + Length of object
Ramu is waiting for a train of 50 meter on a platform of 80 meter. A train passes the platform at the speed of 36 km/hr . Find the time taken to cross the platform.
Answer Total distance travelled = Length of the train + Length of the platform
D = 50+80 = 130 m
V = 36 km/hr = 10 m/sec
Time taken, T = 130/10 = 13 sec
The new case arises when a train passes a moving object eg. car,train,trolly etc.In this situation we use the concept of relative velocity.When the speed is expressed with the respect of a moving object , it is called relative velocity.
A. when two trains are moving in the same direction with speed S1 and S2 .Relative speed = S1 – S2 (S1>S2)
B.When two trains are approaching each other ,Relative speed = S1+S2
Two trains of length 50 m and 25 m are approaching each other at the speed of 36 km/hr and 54 km/hr.find the time taken to cross each other.
Since, trains are approaching so relative speed = 10 m/sec + 15 m/sec = 25 m/sec
Total Distance = 50 m +25 m = 75 m
So time taken = (D/S) = 3 sec
Note- The same question can be asked given trains are moving in the same direction.Relative speed will be the difference of two speeds.
Relative Speed = 15 m/sec – 10 m/sec = 5 m/sec
Time taken = (D/S) = (75/5) = 15 sec
Summary of Problems on trains
St=Speed of the train , So=Speed of object , Lt=Length of train , Lo =Length of the object
Case 1 Train crossing a stationary object without length
St * t= Lt
Case 2 Train crossing an object with length
St * t = Lt+Lo
Case 3 Train cossing a moving object without length
In opposite direction (St+So) * t = Lt
In same direction (St-So) * t = Lt
Case 4 Train crossing a moving object with length
In opposite direction (St+So) * t =Lt + Lo
In same direction (St-So) * t = Lt +Lo
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