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
Relationship between Speed, Distance and Time
Problems on Calculating Distance
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
Two Trains Passes in the Same Direction
Two Trains Passes in the Opposite Direction
8th Grade Math Practice
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Worksheet on Conversion of Units of Speed
Worksheet on Calculating Speed
Worksheet on Calculating Distance
Worksheet on Train Passes through a Pole
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