Trains( Speed, Distance)


1. Conversion from km/hr to m/s   
xkm/hr= (x\times\frac{5}{{18}}) m/sec

2. Conversion from m/s to km/hr xm/sec= (x\times\frac{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.

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 other\frac{(a+b)}{(u+v)}sec

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 =\frac{(u+v)}{(a+b)}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

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