What is the length of a train which crosses a bridge of 150 m in 20 sec with a speed of 72 km h?

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Speed of train will help us to calculate different types of problems on motion.

1. When a train passes a stationary object:

Let x be the length of the train which includes the engine also. When the end of the train passes the object, then the engine of the train has to move a distance equal to the train.

Then the time taken by the train to pass the stationary object = length of the train/speed of the train

2. When a train passes a stationary object having some length:

When the end of the train passes the stationary object having some length, then the engine of the train has to move a distance equal to the sum of the length of the train and stationary object.

Then the time taken by the train to pass the stationary object = (length of the train + length of the stationary object)/speed of the train

Problems to calculate the motion or speed of train:

1. Find the time taken by a train 150 m long, running at a speed of 90 km/hr in crossing the pole.

Solution:            

Length of the train = 150m

Speed of the train = 90 km/hr

                         = 90 × 5/18 m/sec

                         = 25m/sec

Therefore, time taken by the train to cross the pole = 150 m/25m/sec = 6 seconds.

2. A train 340 m long is running at a speed of 45 km/hr. what time will it take to cross a 160 m long tunnel?

Solution:            

Length of the train = 340 m

Length of the tunnel = 160m

Therefore, length of the train + length of the tunnel = (340 + 160) m = 500m

Speed of the train = 45 km/hr

Speed of the train = 45 × 5/18 m/sec

                         = 25/2 m/sec

                         = 12.5 m/sec

Therefore, time taken by the train to cross the tunnel = 500 m/12.5 m/sec.

= 40 seconds.

3. A train is running at a speed of 90 km/hr. if it crosses a pole in just 10 second, what is the length of the train?

Solution:            

Speed of the train = 90 km/hr

Speed of the train = 90 × 5/18 m/sec = 25 m/sec

Time taken by the train to cross the pole = 10 seconds

Therefore, length of the train = 25 m/sec × 10 sec = 250 m

4. A train 280 m long crosses the bridge 170 m in 22.5 seconds. Find the speed of the train in km/hr

Solution:            

Length of the train = 280 m

Length of the bridge = 170 m

Therefore, length of the train + length of the bridge = 280 m + 170 m = 450 m

Time taken by the train to cross the bridge = 22.5 sec = 45/2 sec.

Therefore, speed of train = 450 m/22.5 m/sec = 450/45/2 m/sec = 20 m/sec

To convert the speed from m/sec to km/hr, multiply by 18/5

Therefore, speed of the train = 20 × 18/5 km/hr = 72 km/hr

Speed of Train

Relationship between Speed, Distance and Time

Conversion of Units of Speed

Problems on Calculating Speed

Problems on Calculating Distance

Problems on Calculating Time

Two Objects Move in Same Direction

Two Objects Move in Opposite Direction

Train Passes a Moving Object in the Same Direction

Train Passes a Moving Object in the Opposite Direction

Train Passes through a Pole

Train Passes through a Bridge

Two Trains Passes in the Same Direction

Two Trains Passes in the Opposite Direction

8th Grade Math Practice

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When the train passes through a bridge or platform or tunnel or a stationary object having some length

If length of train = x meters and length of the stationery object = y meters.

Also, speed of the train is z km/hr, then time taken by the train to pass the stationary object having length y meters.

= (length of the train + length of stationary object)/speed of the train

= (x meters + y meters)/z km/hr

Note: Change km/hr to m/sec.

Solved examples to calculate when the train passes through a bridge or a stationary object having some length.

1. A train 175 m long crosses a bridge which is 125 m long in 80 seconds. What is the speed of the train?

Solution:            

Length of the train = 175 m.       

Length of the bridge = 225 m

Distance covered by the train to cross the bridge = (175 + 225) m

                                                                   = 400 m

Time taken by the train to cross the bridge = 80 seconds

Speed = distance/time

         = 400/80 m/sec

         = 5 m/sec.

2. A train 220 m long is running at a speed of 36 km/hr. What time will it take to cross a 110 m long tunnel?

Solution:            

Length of the train = 220 m

Length of the tunnel = 110 m

Therefore, length of the train + length of the tunnel = (220 + 110) m = 330m

Speed of the train = 36 km/hr   

Speed of the train = 36 × 5/18 m/sec = 10 m/sec

Therefore, time taken by the train to cross the tunnel = 330 m/10 m/sec.

                                                                         = 33 seconds.

3. Find the time taken by 150 m long train passes through a bridge which is 100 m long, running at a speed of 72 km/hr.

Solution:            

Speed of train = 72 km/hr = 72 × 5/18 m/sec = 20 m/sec

In order to cross a bridge of length 100 m, the train will have to cover a distance = (150 + 100) m = 250 m

Thus, speed = 20 m/sec and distance = 250 m

Time = distance/speed

       = 250m/20 m/sec

       = 25/2 sec

       = 12.5 sec.                                                                    

4. A 90 m long train is running at a speed of 54 km/hr. If it takes 30 seconds to cross a platform, find the length of the platform.

Solution:            

Speed of the train = 54 km/hr = 54 × 5/18 m/sec = 15 m/sec

Time taken to cross the bridge = 30 sec

Distance covered by train to cross the platform = speed × time

                                                                = (15 × 30) m

                                                                = 450 m

To cross the platform, train covers a distance = length of train + length of platform

                                                     450 m = 90 m + length of platform

Therefore, length of platform = (450 – 90) m = 360 m

Speed of Train

Relationship between Speed, Distance and Time

Conversion of Units of Speed

Problems on Calculating Speed

Problems on Calculating Distance

Problems on Calculating Time

Two Objects Move in Same Direction

Two Objects Move in Opposite Direction

Train Passes a Moving Object in the Same Direction

Train Passes a Moving Object in the Opposite Direction

Train Passes through a Pole

Train Passes through a Bridge

Two Trains Passes in the Same Direction

Two Trains Passes in the Opposite Direction

8th Grade Math Practice

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