Relative Speed And Train Questions

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RELATIVE SPEEED AND TRAIN QUESTIONS

Speed has no sense of direction unlike the velocity. Relative speed is the speed of one object as observed from another moving object. Questions on train are the classic examples of relative speed and in all these questions it is assumed that trains move parallel to each other – whether in the same direction or the opposite direction. Thus, we shall see how the relative speed is calculated and using it we come to know the time taken by the trains to cross each other and some other like aspects.

Important Formulas – Problems on Trains

1. x km/hr = (x×5)/18 m/s 

2. y m/s = (y×18)/5 km/hr 

3. Speed = distance/time, that is, s = d/t

4. velocity = displacement/time, that is, v = d/t

5. Time taken by a train x meters long to pass a pole or standing man or a post 
   = Time taken by the train to travel x meters.

6. Time taken by a train x meters long to pass an object of length y meters

= Time taken by the train to travel (x + y) metres.

7. Suppose two trains or two objects are moving in the same direction at v1 m/s and v2 m/s where v1 > v2,

then their relative speed = (v1 – v2) m/s

8. Suppose two trains or two objects are moving in opposite directions at v1 m/s and v2 m/s ,

then their relative speed = (v1+ v2) m/s

9. Assume two trains of length x metres and y metres are moving in opposite directions at v1 m/s and v2 m/s, Then

The time taken by the trains to cross each other = (x+y) / (v1+v2) seconds

10. Assume two trains of length x metres and y metres are moving in the same direction at at v1 m/s and v2 m/s where v1 > v2, Then

The time taken by the faster train to cross the slower train = (x+y) / (v1-v2) seconds

11. Assume that two trains (objects) start from two points P and Q towards each other at the same time and after crossing they take p and q seconds to reach Q and P respectively. Then,

A’s speed: B’s speed = √q: √p

Solved Examples

Level 1

Explanation :

Speed of the train, v = 40 km/hr = 40000/3600 m/s = 400/36 m/s 

Time taken to cross, t = 18 s 

Distance Covered, d = vt = (400/36)× 18 = 200 m 

Distance covered is equal to the length of the train = 200 m

Answer : Option C

Explanation :

v = 240/24 (where v is the speed of the train) = 10 m/s

t = (240+650)/10 = 89 seconds

Answer : Option A

Explanation :

Distance = 140+160 = 300 m

Relative speed = 60+40 = 100 km/hr = (100×10)/36 m/s 

Time = distance/speed = 300 / (100×10)/36 = 300×36 / 1000 = 3×36/10 = 10.8 s

Answer : Option A

Explanation :

Let x is the length of the train and v is the speed

Time taken to move the post = 8 s 

=> x/v = 8 

=> x = 8v — (1)

Time taken to cross the platform 264 m long = 20 s

(x+264)/v = 20

=> x + 264 = 20v —(2)

Substituting equation 1 in equation 2, we get

8v +264 = 20v

=> v = 264/12 = 22 m/s

= 22×36/10 km/hr = 79.2 km/hr

Answer : Option C

Explanation :

Ratio of their speeds = Speed of first train : Speed of second train

= √16: √ 9

= 4:3

Answer : Option D

Explanation :

Relative speed = 120+80 = 200 kmph = 200×10/36 m/s = 500/9 m/s

time = 9s

Total distance covered = 270 + x where x is the length of other train

(270+x)/9 = 500/9

=> 270+x = 500

=> x = 500-270 = 230 meter

Answer : Option B

Explanation :

Assume both trains meet after x hours after 7 am

Distance covered by train starting from P in x hours = 20x km

Distance covered by train starting from Q in (x-1) hours = 25(x-1)

Total distance = 110

=> 20x + 25(x-1) = 110

=> 45x = 135

=> x= 3 Means, they meet after 3 hours after 7 am, ie, they meet at 10 am

Answer : Option B

Explanation :

Distance covered = 120+120 = 240 m

Time = 12 s

Let the speed of each train = v. Then relative speed = v+v = 2v

2v = distance/time = 240/12 = 20 m/s

Speed of each train = v = 20/2 = 10 m/s 

= 10×36/10 km/hr = 36 km/hr

Level 2

Answer : Option B

Explanation :

Assume the length of the bridge = x meter

Total distance covered = 130+x meter

total time taken = 30s

speed = Total distance covered /total time taken = (130+x)/30 m/s

=> 45 × (10/36) = (130+x)/30

=> 45 × 10 × 30 /36 = 130+x

=> 45 × 10 × 10 / 12 = 130+x

=> 15 × 10 × 10 / 4 = 130+x

=> 15 × 25 = 130+x = 375

=> x = 375-130 =245

Answer : Option A

Explanation :

Length of the train, l = 150m 

Speed of the man, Vm= 2 km/hr 

Relative speed, Vr = total distance/time = (150/3) m/s = (150/3) × (18/5) = 180 km/hr 

Relative Speed = Speed of train, Vt – Speed of man (As both are moving in the same direction) 

=> 180 = Vt – 2  => Vt = 180 + 2 = 182 km/hr

Answer : Option D

Explanation :

Let the speed of the trains be x and y respectively 

length of train1 = 27x

length of train2 = 17y

Relative speed= x+ y

Time taken to cross each other = 23 s

=> (27x + 17 y)/(x+y) = 23 => (27x + 17 y)/ = 23(x+y)

=> 4x = 6y => x/y = 6/4 = 3/2

Answer : Option B

Explanation :

Distance to be covered = 240+ 120 = 360 m

Relative speed = 36 km/hr = 36×10/36 = 10 m/s

Time = distance/speed = 360/10 = 36 seconds

Answer : Option C

Explanation :

Speed of the train = 54 km/hr = (54×10)/36 m/s = 15 m/s

Length of the train = speed × time taken to cross the man = 15×20 = 300 m

Let the length of the platform = L

Time taken to cross the platform = (300+L)/15 

=> (300+L)/15 = 36

=> 300+L = 15×36 = 540 => L = 540-300 = 240 meter

Answer : Option C

Explanation :

Let x is the length of the train in meter and v is its speed in kmph

x/9 = (v-2) (10/36) — (1)

x/10 = (v-4) (10/36) — (2)

Dividing equation 1 with equation 2

10/9 = (v-2)/(v-4) => 10v – 40 = 9v – 18 => v = 22

Substituting in equation 1, x/9 = 200/36  => x = 9×200/36 = 50 m

Answer : Option D

Explanation :

Speed of train1 = 48 kmph

Let the length of train1 = 2x meter

Speed of train2 = 42 kmph

Length of train 2 = x meter (because it is half of train1’s length)

Distance = 2x + x = 3x

Relative speed= 48+42 = 90 kmph = 90×10/36 m/s = 25 m/s

Time = 12 s

Distance/time = speed => 3x/12 = 25 

=> x = 25×12/3 = 100 meter

Length of the first train = 2x = 200 meter

Time taken to cross the platform= 45 s

Speed of train1 = 48 kmph = 480/36 = 40/3 m/s

Distance = 200 + y where y is the length of the platform

=> 200 + y = 45×40/3 = 600

=> y = 400 meter

Answer : Option B

Explanation :

Distance = 800+x meter where x is the length of the tunnel

Time = 1 minute = 60 seconds

Speed = 78 km/hr = 78×10/36 m/s = 130/6 = 65/3 m/s

Distance/time = speed

(800+x)/60 = 65/3 => 800+x = 20×65 = 1300

=> x = 1300 – 800 = 500 meter

Answer : Option B

Explanation :

Relative speed = 40-20 = 20 km/hr = 200/36 m/s = 100/18 m/s

Time = 5 s

Distance = speed × time = (100/18) × 5 = 500/18 m = 250/9 = 2779 m = length of the fast train

,

Relative speed is the speed of one object relative to another. It is calculated by subtracting the speeds of the two objects. For example, if a train is moving at 100 miles per hour and another train is moving at 50 miles per hour, the relative speed of the two trains is 50 miles per hour.

Train questions are a type of math problem that involves calculating the speed, distance, or time of a train. They can be challenging, but they can also be fun to solve. There are many different types of train questions, but some of the most common include:

• Train chasing: In this type of question, two trains are moving in opposite directions. The question asks how long it will take for the first train to catch up to the second train.
• Train overtaking: In this type of question, two trains are moving in the same direction. The question asks how long it will take for the first train to overtake the second train.
• Train crossing: In this type of question, two trains are moving on parallel tracks. The question asks how long it will take for the trains to pass each other.
• Train meeting: In this type of question, two trains are moving on converging tracks. The question asks how far apart the trains will be when they meet.

Train problems are a type of physics problem that involves calculating the forces and energy of a train. They can be challenging, but they can also be fun to solve. There are many different types of train problems, but some of the most common include:

• Train braking: In this type of problem, a train is moving at a certain speed and then needs to stop. The question asks how much force is needed to stop the train.
• Train accelerating: In this type of problem, a train is at rest and then needs to start moving. The question asks how much force is needed to accelerate the train.
• Train climbing: In this type of problem, a train is moving up a hill. The question asks how much force is needed to overcome the force of gravity and keep the train moving.
• Train descending: In this type of problem, a train is moving down a hill. The question asks how much force is needed to keep the train from going too fast.

Train chasing, overtaking, crossing, and meeting are all examples of relative speed problems. In each of these problems, there are two trains moving at different speeds. The question is how long it will take for one train to catch up to, overtake, cross, or meet the other train.

To solve a relative speed problem, you need to know the speeds of the two trains and the distance between them. You can then use the following formula to calculate the time it will take for one train to catch up to, overtake, cross, or meet the other train:

Time = Distance / Relative Speed

For example, if one train is moving at 100 miles per hour and another train is moving at 50 miles per hour, and the distance between them is 100 miles, it will take 2 hours for the first train to catch up to the second train.

Train questions and problems can be challenging, but they can also be fun to solve. With a little practice, you can learn how to solve even the most difficult problems.

Here are some frequently asked questions and short answers about relative speed and train questions:

• What is relative speed?
  Relative speed is the speed of one object relative to another object. It is calculated by subtracting the speeds of the two objects. For example, if a car is traveling at 60 miles per hour and a train is traveling at 40 miles per hour, the relative speed of the car to the train is 20 miles per hour.

• How do you calculate relative speed?
  To calculate relative speed, you need to know the speeds of the two objects and the direction of travel. If the two objects are traveling in the same direction, the relative speed is the difference between their speeds. If the two objects are traveling in opposite directions, the relative speed is the sum of their speeds.

• What are some examples of relative speed?
  Some examples of relative speed include:

• The speed of a car relative to a train.

• The speed of a ball relative to a bat.
• The speed of a runner relative to a walker.

• The speed of a cyclist relative to a pedestrian.

• What are some train questions?
  Some train questions include:

• How long does it take a train to travel from one station to another?

• What is the top speed of a train?
• How many passengers can a train carry?
• What are the different types of trains?

• What are the safety features of a train?

• What are some frequently asked questions about relative speed and train questions?
  Some frequently asked questions about relative speed and train questions include:

• What is the difference between relative speed and absolute speed?

• How does relative speed affect the time it takes for two objects to meet?
• What are some real-world examples of relative speed?
• What are some of the factors that affect the speed of a train?
• What are some of the safety features of a train?

Sure, here are some MCQs without mentioning the topic Relative Speed And Train Questions:

1. A car travels 100 miles in 2 hours. What is the Average speed of the car?
2. A train travels 200 miles in 4 hours. What is the average speed of the train?
3. A plane travels 300 miles in 1 hour. What is the average speed of the plane?
4. A boat travels 400 miles in 2 hours. What is the average speed of the boat?

5. A bicycle travels 500 miles in 5 hours. What is the average speed of the bicycle?

6. A car travels 100 miles in 2 hours. If the car’s speed is constant, what is the car’s speed in miles per hour?

7. A train travels 200 miles in 4 hours. If the train’s speed is constant, what is the train’s speed in miles per hour?
8. A plane travels 300 miles in 1 hour. If the plane’s speed is constant, what is the plane’s speed in miles per hour?
9. A boat travels 400 miles in 2 hours. If the boat’s speed is constant, what is the boat’s speed in miles per hour?

10. A bicycle travels 500 miles in 5 hours. If the bicycle’s speed is constant, what is the bicycle’s speed in miles per hour?

11. A car travels 100 miles in 2 hours. If the car’s speed is increasing, what is the car’s speed at the end of the first hour?

12. A train travels 200 miles in 4 hours. If the train’s speed is increasing, what is the train’s speed at the end of the first hour?
13. A plane travels 300 miles in 1 hour. If the plane’s speed is increasing, what is the plane’s speed at the end of the first half hour?
14. A boat travels 400 miles in 2 hours. If the boat’s speed is increasing, what is the boat’s speed at the end of the first hour?

15. A bicycle travels 500 miles in 5 hours. If the bicycle’s speed is increasing, what is the bicycle’s speed at the end of the first hour?

16. A car travels 100 miles in 2 hours. If the car’s speed is decreasing, what is the car’s speed at the end of the first hour?

17. A train travels 200 miles in 4 hours. If the train’s speed is decreasing, what is the train’s speed at the end of the first hour?
18. A plane travels 300 miles in 1 hour. If the plane’s speed is decreasing, what is the plane’s speed at the end of the first half hour?
19. A boat travels 400 miles in 2 hours. If the boat’s speed is decreasing, what is the boat’s speed at the end of the first hour?
20. A bicycle travels 500 miles in 5 hours. If the bicycle’s speed is decreasing, what is the bicycle’s speed at the end of the first hour?