# Trains( Speed, Distance)

1. Conversion from km/hr to m/s
xkm/hr=  m/sec

2. Conversion from m/s to km/hr xm/sec=  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.

EgA train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the length of the train?

Sol: We have to convert km/hr into m/sec, as the other given instruction is in seconds.

60km/hr= 60*5/18 => 50/3 ( don’t convert it into decimals in this stage in any problem)

speed = dist/time => 50/3= D/9  => D= 150m

4. Time taken by a train of length l metres to pass a stationery object of length b metres 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 u m/s and v m/s, where u > v, then their relative speed is = (u – v) m/s.

Eg: A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is:

Sol: Speed of Train relative to Man is 125/10 m/sec;

Relative means, if a man stands and watch the train. For him, the train moves in 10 sec therfore (for him) the train speed is 125/10 = 25/2 m/sec

25/2 * 8/15 = 45km/hr ( Converted into km/hr)

The above one is the speed of the train relative to man, the original speed- man’s speed=relative speed ( Same Direction)

x-5=45; => x=50;

Therefore, 50km/hr

6. Suppose two trains or two objects 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 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 othersec

Please note this is just formula of time which is distance upon speed.

We are just adding two distances and two speeds

8. 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 =sec

Please note as trains are moving in the same directions so we used (u-v)

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:

(Aspeed):(Bspeed)=(b:a)

# Practice Here

September 10, 2013