## Problems on Train

### Important Formulae

1. km/hr to m/s conversion: a km/hr = (a x 5/18)m/s

2. m/s to km/hr conversion: a m/s = (a x 18/5)km/hr

3. Time taken by a train of length l metres to pass a pole or standing man or a signal post is equal to the time taken by the train to cover l metres.

4. Time taken by a train of length l metres to pass a stationery object of length bmetres is the time taken by the train to cover (l + b) metres.

5. Suppose two trains or two objects bodies are moving in the same direction at um/s and v m/s, where u > v, then their relative speed is = (u - v) m/s.

6. Suppose two trains or two objects bodies are moving in opposite directions at um/s and v m/s, then their relative speed is = (u + v) m/s.

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

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

9. If two trains (or bodies) 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)

### General Tips

Question 1

What is the time taken by a train of length ‘L’ metres and travelling at a speed of ‘S’ to pass a pole or a standing man or a signal post or some stationary object?**
Explanation**

• The Question will contain length of the train ‘L’

• Train’s speed ‘S’ will be given in terms of either km/hr or m/sec

If speed is given in terms of Km/hr, always remember to convert it to m/sec which can be done by this formula: =S x (5/18) m/sec

• You have to find the time taken by the train to pass the stationary object. Use this formula
Time taken to pass the object= L/S sec

Question 2

What is the time taken by a train of length ‘L’ metres and travelling at speed of ‘S’ to pass a pole or a standing man or a signal post or some stationary object of Length ‘M’?

Explanation

• The Question will contain length of the train ‘L’

• Length of the object ‘M’

• Train’s speed ‘S’ will be given in terms of either km/hr or m/sec.

If the speed is given in terms of Km/hr, always remember to convert it to m/sec which is done by this formula: =S x (5/18) m/sec

• You have to find the time taken by the train to pass the object of length ‘M’. Follow this procedure

1. You know this: Time taken to pass the object= L/S sec

2. Make changes to the above formula in this way

Time taken to pass the object of length ‘M’ = (L+M)/S sec

Question 3

What is the taken by the two trains that are of length ‘a’ and ‘b’ respectively and travelling in the same direction or parallel to each other at a speed of ‘u’ and ‘v’ respectively to cross each other?

Explanation

• The Question will contain two trains and its lengths as: ‘a’ of the first train and ‘b’ of the second train.

• The speed of the trains will also be included as ‘u’ as speed of the first train and ‘v’ as the speed of the second train

If the speed is given in terms of Km/hr, always remember to convert it to m/sec which is done by this formula

For train 1: =u x (5/18) m/sec and

For train 2: = v x (5/18) m/sec

Or

= (u+v) x (5/18) m/sec

• Now you have find out the time taken by the trains to cross each other; use this formula

= (a+b)/ (u-v)

u-v is called as relative speed of trains travelling in opposite direction

Question 4

What is the time taken by the two trains that start at their points: A for the first train and B for the second train that travels at a speed of ‘u’ and ‘v’ respectively to reach their destination after crossing each other?

Explanation

• The Question will contain two trains and its’ Speed as: ‘u’ of the first train and ‘v’ of the second train.

• You have to find out the time taken by the trains to reach their destination after crossing each other.

Use this formula
(√v: √u)

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