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Important Formulae

1. km/hr to m/s conversion
y km/hr = y x 5/18m/s.

2. m/s to km/hr conversion
y m/s = y x 18/5km/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 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.

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 = (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.

Practice Questions

1.

 What is the time taken by a train running at 54 kmph to cross a man standing on a platform, the length of the train being 180 m ? A.10 seconds B.12 seconds C.14 seconds D.16 seconds

Speed of train = 54 kmph = 54 x 5/18 = 15 m/s.
Distance = length of the train = 180 m.
∴ Time = 180/15 = 12 seconds.

2.

 How long will a train 100 m long and travelling at a speed of 45 kmph, take to cross a platform of length 150 m? A.24 seconds B.18 seconds C.20 seconds D.22 seconds

Distance = length of the train + length of the platform.
distance = 100 + 150 = 250 m.
⇒ 45 x 5/18 = 12.5 m
∴ Time = 250/12.5 = 20 seconds.

3.

 Find the length of the bridge, which a train 120 m long travelling at 54 kmph can cross in 30 seconds. A.330 m B.320 m C.310 m D.340 m

Speed of the train = 54 kmph.
⇒ 54 x 5/18 = 15 m/s
∴ distance covered in 30 seconds.
⇒ 15 x 30 = 450 m
length of bridge = distance covered – length of train.
Hence, length of bridge = 450 – 120 = 330 m

4.

 Find the time taken by a train 150 m long running at a speed of 63 kmph to cross another train of length 100 m running at a speed of 45 kmph in the same direction. A.45 seconds B.60 seconds C.55 seconds D.50 seconds

Total distance covered = sum of length of the two train = 100 + 150 = 250 m
Relative speed of the two trains = 63 – 45 = 18 kmph
(since the trains are running in the same direction the relative speed will be the difference in the speeds).
⇒ 18 x 5/18 = 5 m/s
∴ Time = 250/5 = 50 seconds

5.

 A train crosses two persons, cycling in the same direction as the train in 12 and 18 seconds respectively. If the speeds of the two cyclists are 9 and 18 kmph respectively, find the length and the speed of the train. A.90 m , 36 kmph B.96 m , 34 kmph C.94 m , 38 kmph D.95 m , 40 kmph

Let the speed of train is s kmph
Relative speed of overtaking first cyclists = (s – 9) kmph
Time took to overtake the first cyclist = 12 seconds
∴ length of train = 12 x (s – 9) x 5/18 →(i)
Similarly, considering the case of overtaking the second cyclist,
∴ length of train = 18 x (s - 18) x 5/18 →(ii)
Equating (i) and (ii),
⇒ 12 x (s – 9) x 5/18 = 18 x (s – 18) x 5/18
⇒ 2s – 18 = 3s – 54
⇒ s = 36 kmph.
Now, length = 12 x (s – 9) x 5/18 = 12 x 27 x 5/18
∴ length = 90 m

6.

 How long does a train 120 m long running at the speed of 72 kmph take to cross a bridge 130 m in length? A.9.8 sec B.12.5 sec C.11.5 sec D.14.3 sec

Speed = (72 x 5/18) m/s = 20 m/s.
Total distance covered = (120 + 130) m = 250 m
∴ Required time = (250/20) sec = 12.5 sec.

7.

 A train 260 m long is running at a speed of 45 kmph. In what time will it pass a bridge 240 m long? A.40 seconds B.42 seconds C.45 seconds D.48 seconds

Speed = 45 x (5/18) m/s = 25/2 m/s
Total distance covered = (260 + 240) m = 500 m
∴ Required time = 500 x (2/25) sec = 40 sec.

8.

 A train running at the speed of 60 kmph crosses a pole in 18 seconds. What is the length of the train? A.200 m B.300 m C.324 m D.CBD

Speed = 60 x (5/18) m/s = (50/3) m/s.
Length of the train = (Speed x Time) = (50/3 x 18) m = 300 m.