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 metres to pass a
pole or a standing man or a signal post is
equal to the time taken by the train to cover 1 metres.
4.
Time taken by a train of length 1 metres to pass a stationary object of
length b metres is the time taken
by the train to cover (1 + b) metres.
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 metres and b metres
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 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.
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 speet) :
(B’s speed) = (b1/2: a1/2).
SOLVED EXAMPLES
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
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
Ex. 3. A man is standing on a railway bridge which is 180 m long. He finds that a train crosses the bridge in 20 seconds but himself in 8 seconds. Find the length of the train and its speed?
Sol. Let the length of the train be x metres,
Then, the train covers x metres in 8 seconds and (x + 180) metres in 20 sec
x/8=(x+180)/20 รณ 20x = 8 (x + 180) <=> x = 120.
Length of the train = 120 m.
Speed of the train = (120/8) m / sec = m / sec = (15 *18/5) kmph = 54 km
Sol: Speed of the train relative to man = (68 - 8) kmph
= (60* 5/18) m/sec = (50/3)m/sec
Time taken by the train to cross the man I
= Time taken by It to cover 150 m at 50/3 m / sec = 150 *3/ 50 sec = 9sec
Ex. 5. A train 220 m long is running with a speed of 59 kmph In what will it pass a man who is running at 7 kmph in the direction opposite to that in which the train is going?
sol. Speed of the train relative to man = (59 + 7) kmph
= 66 *5/18 m/sec = 55/3 m/sec.
Time taken by the train to cross the man = Time taken by it to cover 220 m at (55/3) m / sec = (220 *3/55) sec = 12 sec
=(90*5/18) m / sec = 25 m /sec.
Time taken by the trains to'pass each other
= Time taken to cover (137 + 163) m at 25 m /sec =(300/25) sec = 12 sec
Sol: Relative speed of the trains = (72 - 54) km/hr = 18 km/hr
= (18 * 5/18) m/sec = 5 m/sec.
Time taken by the trains to cross each other
= Time taken to cover (100 + 120) m at 5 m /sec = (220/5) sec = 44 sec.
Sol:Let the speed of the train be x kmph.
Speed of the train relative to man = (x + 5) kmph = (x + 5) *5/18 m/sec.
Therefore 100/((x+5)*5/18)=6 <=> 30 (x + 5) = 1800 <=> x = 55
Speed of the train is 55 kmph.
Ex9. A train running at 54 kmph takes 20 seconds to pass a platform. Next it takes.12 sec to pass a man walking at 6 kmph in the same direction in which the train is going . Find the length of the train and the length of the platform.
Sol: Let the length of train be x metres and length of platform be y metres.
Speed of the train relative to man = (54 - 6) kmph = 48 kmph
= 48*(5/18) m/sec = 40/3 m/sec.
In passing a man, the train covers its own length with relative speed.
Length of train = (Relative speed * Time) = ( 40/3)*12 m = 160 m.
Also, speed of the train = 54 *(5/18)m / sec = 15 m / sec.
(x+y)/15 = 20 <=> x + y = 300 <=> Y = (300 - 160) m = 140 m.
Ex10. A man sitting in a train which is traveling at 50 kmph observes that a goods train, traveling in opposite direction, takes 9 seconds to pass him. If the goods train is 280 m long, find its speed.?
Sol: Relative speed = 280/9 m / sec = ((280/9)*(18/5)) kmph = 112 kmph.
Speed of goods train = (112 - 50) kmph = 62 kmph.
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