PROBLEMS ON TRAINS

IMPORTANT FACTS AND FORMULAE

1. a km/hr= (a* 5/18) m/s.
2. a m / s = (a*18/5) km/hr.
3. Time taken by a train of length 1 meters to pass a pole or a standing man or a signal  post is equal to the time taken by the train to cover 1 meters.
4. Time taken by a train of length 1 meters to pass a stationary object of length  b meters is the time taken by the train to cover (1 + b) meters.
5. Suppose two trains or two bodies are moving in the same direction at u m / s and v m/s, where u > v, then their relatives speed = (u - v) m / s.
6. Suppose two trains or two bodies are moving in opposite directions at u m / s and v m/s, then their relative speed is = (u + v) m/s.
7. If two trains of length a meters and b meters are moving in opposite directions at u  m / s and v m/s, then time taken by the trains to cross each other =  (a + b)/(u+v) sec.
8. If two trains of length  a meters and b meters 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. 
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^1/2: a^1/2)

Ex.I. A train 100 m long is running at the speed of 30 km / hr. Find the time taken  by it to pass a man standing near the railway line.

Sol. Speed of the train = (30 x 5/18_) m / sec = (25/3) m/ sec.

        Distance moved in passing the standing man = 100 m.

       Required time taken = 100/(25/3) = (100 *(3/25)) sec = 12 sec

Ex. 2. A train is moving at a speed of 132 km/br. If the length of the train is 110 metres, how long will it take to cross a railway platform 165 metres long?

Sol. Speed of train = 132 *(5/18) m/sec = 110/3  m/sec.

    Distance covered in passing the platform = (110 + 165) m = 275 m.

       

       Time taken =275 *(3/110)  sec =15/2 sec = 7  ½ sec