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A train, 130 m long crosses a platform in 30 sec with a speed of 45km/h. What is the length of the platform?

Last updated date: 22nd Feb 2024
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IVSAT 2024
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Hint: In this particular question use the concept of speed, distance and time which is related as, $ {\text{speed}} = \dfrac{{{\text{distance}}}}{{{\text{time}}}} $ , and assume any variable be the length of the platform in meters and use the concept that in 1 km there is 1000 m and in 1 hour there is 60 minutes so use these concepts to reach the solution of the question.

Complete step-by-step answer:
Given data:
Length of the train, L = 130 m
Crosses a platform in 30 sec, with a speed of 45Km/hr.
Let, t = 30 sec.
And, v = 45 km/hr.
As we know that 1 km = 1000 m and 1 hr. = 60 min = 3600 sec.
So 45 km/hr. = $ \dfrac{{45\left( {1000} \right)}}{{3600}} = \dfrac{{450}}{{36}} = \dfrac{{25}}{2} $ m/s.
Therefore, v = $ \dfrac{{25}}{2} $ m/s.
Now as we know that speed, distance and time is related as, $ {\text{speed}} = \dfrac{{{\text{distance}}}}{{{\text{time}}}} $
 $ \Rightarrow v = \dfrac{D}{t} $ ............. (1)
Let the length of the platform be L’ meters.
So the total distance (D) train has to be covered in 30 sec = L + L’ = 130 + L’ meters.
 $ \Rightarrow D = 130 + L' $
Now substitute the values in equation (1) we have
 $ \Rightarrow \dfrac{{25}}{2} = \dfrac{{130 + L'}}{{30}} $
Now simplify it we have,
 $ \Rightarrow \dfrac{{25}}{2}\left( {30} \right) = 130 + L' $
 $ \Rightarrow L' = \dfrac{{25}}{2}\left( {30} \right) - 130 = 375 - 130 = 245 $ Meters.
So this is the required length of the platform.

Note: Whenever we face such types of questions the key concept we have to remember is that as the units of speed is given is km/hr. unit of time is in sec and unit of length of train in meters so if we directly substitute these values into the formula then there is a mismatch in the units, so first we have to change the unit of speed to m/s from km/hr. as above then substitute these values in the formula and simplify as above we will get the required answer, always remember that the total distance covered by the train is the sum of length of the platform and the length of the train.