Problem on Train 🚂

📝Topic: Problem on Train

📝Introduction:

Train-a problem te hian maths leh physics-ah hmun pawimawh tak a luah a ni. Heng a hnuai ah te hian point pawimawh tak takte leh hrilhfiahna a

dah a ni:

Rel chungchang harsatnate hian relative speed, hlat zawng, leh hun te a tel tlangpui a, an kalna kawng pangngai an zawh a, an speed a inang lo thin.

🤷Eng nge relative speed chu?

🕵️Relative speed hi object pahnih emaw a aia tam emaw an kal chak dan leh kawng a zir a ni. Object pahnih an kal chak dan leh kawng a zir a, an inkalh chhawk dan a ni.

Entirnan:

- Car A a kal chak dan 60 km/hr, Car B a kal chak dan 40 km/hr a nih chuan:

- An kalna kawng inang a nih chuan, Relative Speed = 60 + 40 = 100 km/hr

- An kalna kawng inang lo a nih chuan, Relative Speed = 60 - 40 = 20 km/hr

✅ Rel Chungchang Harsatnaa Pawimawh Te:

1.Rel Sei Zawng: Rel chungchang harsatnaah hian, rel sei zawng hi thil pawimawh tak a ni a, relin thil pakhat emaw rel dang a paltlang hun chhung tur a hril thin.

🕵️Paltlang Tura Hun Hman:

Relin thil ding ding reng (entirnan, ban) a paltlangin, a kal hlat zawng chu rel sei zawng nen a intluk a, chhan chu Mihring, car, Dog, cat, horse, Tree, Pole, etc sei zawng hi Rel sei zawng nen a khaikhin theih loh vang a ni.

Relin thil dang che (rel dang ang) a paltlangin, hun hman zat chu an relative speed leh an rel sei zawng zawm khawm a zirin a danglam thin.

🤷Relative Speed:

Thil pahnih an kalna direction a inang chuan, an relative speed chu an speed danglamna a ni.

Thil pahnih an kalna direction a inang lo chuan, an relative speed chu an speed zawm khawm a ni.

Relative speed hi rel an innghak tawn emaw an intlan pel dawn emaw lai vela an speed a pawimawh hle.

✅Case 1: Relin thing/mihring/ban a paltlang:

Chung tiang hun ah chuan time chu a hnuaia formula hmang hian kan zawng chhuak thei ang:

Where,

Example 1: A 335-meter-long train crosses a pillar in 18 seconds Find the speed of the train in km/hr.

Solution:

Given:

Length of the train (Distance) = 335 meters Time taken to cross the pillar = 18 seconds

Step 1: Calculate Speed in m/s Speed Distance/Time = 335/18 18.61 m/s

Step 2: Convert Speed to km/hr To convert m/s to km/hr, we multiply by 3.6: Speed in km/h

18.61x3.6= 67 km/h

The correct answer is 67km/h

✅Case 2: Relin a mihring emaw thildang a Paltlang lai in:

1🤷.Mi tu emaw chu train tlan na lam zawng ang chiah a a tlan ve chuan:

He thilah hi chuan, relative speed kan zawng dawn chuan train chak zawng - mi tu emaw tlan chak zawng.

A time ve thung chu hetiang hian

Where:

L_train Length of the train

S_person Speed of the train

S_train Speed of the person

Hentiang ang case ah problem awm thin te en leh lawk ang

Example 2: A train 100 m long is running at a speed of 70 km per hour. In how much time will it pass a man who is running at 10 km per hour in the same direction in which the train is going?

Solution:

Given:

Train length 100 m Speed of the train 70 kmph

Speed of the person 10 kmph

🕵️Concept used:

While a train crosses a person, it crosses its own length.

Relative speed is the difference between their individual speeds while two objects are running in the same direction.

Timex Speed = Distance 1m/s 18/5 km/h

🤔Calculation:

70 km/hr 70+ (18/5) = 175/9 meter per second 10 km/hr 10+ (18/5)=25/9 meter per second The relative speed of the train 175/9-25/9 = 150/9 meters per second Now, time taken by the train to pass the man 100+ (150/9) 6 seconds

... The correct answer is 6 seconds.

2.🤷Rel Kalna lam hawi lova mi tu emaw a kal H

hunin:

He thil thlen danah hian, an inkungkaih speed chu rel speed leh mi tu emaw speed belhkhawm a ni.

Tun ah hetiang ang type problem lo en ho leh ta ila:

🕵️Example 3: A train running at a speed of 84 km/hr passes a man walking in the opposite direction at the speed of 6 km/hr in 4 seconds. What is the length of the train (in meters)?

Solution:

Speed of the train = 84 km/hr. Speed of man = 6 km/hr.

Relative speed = 84 + 6 ['man is walking in opposite direction] = 90 km/hr 90(1000/3600) = 25m/sec.

Time taken = 4 sec.

Distance = speed x time Here, the distance will be the length of the train. L= 25 x 4 = 100 m.

The correct answer is 100.

✅ Case 3:

🤷 Relin platform/bridge/tunnel a paltlang lai in:

Relin thil che sawn lo (platform emaw bridge emaw ang) a paltlangin, a kal zawng chu rel thui zawng leh platform emaw bridge thui zawng a belhkhawm a ni, an length chu rel length nen a inmil tlat avangin.

🕵️Kal chin zawng = Rel length + Platform/bridge/tunnel length

A time kan zawn chhuah ve dawn thung chuan

Example 4: How long does a train 110 m long running at a speed of 72 km/h take to cross a bridge 132 meters in length?

Solution:

Length of the train = 110 m

Length of the bridge = 132 m

Speed of the train = 72 km/hr = 72 x (5/18) = 20 m/sec

As we know, Time = Distance/Speed Time = (110 + 132)/20

→Time = 242/20

Time = 12.1 seconds

The correct answer is 12.1 seconds.

✅Case 4: Rel pakhatin rel dang a tlan pelh dan

1) 🕵️Rel pahnihte chu kawng hmun khat an zawh theih dan:

Rel pahnih kawng hmun khata an tlan laiin, an relative speed chu rel tlan chak zawk atanga rel tlan muang zawk paihin an chhut chhuak thin.

Tun ah chuan hetiang ang type Questions kan lo en tawh ang:

2) 🤷Rel pahnih an insulkalh hunin:

Rel pahnih an insulkalh hunah, an relative speed chu an chak zawng ve ve belhkhawm a ni.

🕵️Hetiang ang type Questions lo en leh ta ila:

Example 7: Two trains, one is 121 m in length at the speed of 40 km/hour and the other is of 99 m in length at the speed of 32 km/hour are running in opposite directions. In how much time will they be completely clear from each other from the moment they meet?

Solution:

🕵️Important Point

As the faster train is crossing a person sitting in the slower train then the faster train has to cover a distance equal to its own length with relative speed.

Time in which a faster train crosses the man sitting in a slower train = Relative speed/length of Faster train.

✅Practice Questions:

Q1.A train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the length of the train?

A.120 metres

B.180 metres

C.324 metres

D.150 metres

Q2.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:

A.45 km/hr

B.50 km/hr

C.54 km/hr

D.55 km/hr

Q3.The length of the bridge, which a train 130 metres long and travelling at 45 km/hr can cross in 30 seconds, is:

A.200 m

B.225 m

C 245 m

D.250 m

Q4.Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. The ratio of their speeds is:

A.1 : 3

B.3 : 2

C.3 : 4

D.None of these

5.A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?

A.120 m

B.240 m

C.300 m

D.None of these

🤷🕵️🕵️Answer and Explanations:

1. Ans: