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Trains

Important Points :

(1) . When two trains are going in the same direction, then their relative speed is the difference between the two speeds.

Let their speeds are x km/h and y km/h then their relative speed will be (x-y) km/h, x > y,    When two trains are moving in same direction, then their speed will be subtracted.

(2) . When two trains are moving in the opposite direction, then their relative speed is the sum of the two speeds.

Let their speeds are x km/h and y km/h then their relative speed will be (x+y) km/h,    When two trains are moving in opposite directions, then their speed will be added.

(3) . When a train crosses a stationary man/ pole/ lamp post/ sign post- in all these cases, the object which the train crosses is stationary and the distance travelled is the length of the train.

(4) . When it crosses a platform/ bridge- in these cases, the object which the train crosses is stationary and the distance travelled is the length of the train and the length of the object.

(5) . When a train crosses a car/ bicycle/ a mobile man- in these cases, the relative speed between the train and the object is taken depending upon the direction of the movement of the other object relative to the train- and the distance travelled is the length of the train.

(6) .km/hr to m/s conversion:

akm/hr = (a x
5/18
)m/s

(7) . m/s to km/hr conversion:

am/s = (a x
18/5
)km/hr

(8) . If two trains of length a metres and b metres are moving in opposite directions at u m/s and v m/s, then: The time taken by the trains to cross each other =
a+b/u+v
sec

(9) . If two trains of length a metres and b metres are moving in the same direction at u m/s and v m/s, then: The time taken by the faster train to cross the slower train =
a+b/u-v
sec

(10) . If two trains start at the same time from points A and B towards each other and after crossing they take a and b sec in reaching B and A respectively, then:

(A's speed) : (B's speed) = (√b : √a)

(11).If the ratio of the speeds of A and B is a : b, then the ratio of the the times taken by then to cover the same distance is b : a .

(12) . Suppose a train covers a certain distance at x km/hr and an equal distance at y km/hr. Then, the average speed during the whole journey is
2xy/x+y
km/hr