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# A train length $150$meters taken $40.5$ seconds to cross a tunnel of length $300$ meters. What is the speed of the train in$km/hr$?A.$40km/hr$B.$26.67km/hr$C.$50km/hr$D.$66.67km/hr$

Last updated date: 09th Aug 2024
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Hint: First of all we need to know that when a train crosses any object then it will cover the distance of its length and length of that object. Simple train problems are based on kinematics of motion of objects. Here we will use speed formula which is ${\text{speed}} = \dfrac{{{\text{total distance}}}}{{{\text{time}}}}$.

In the question we have given that,
Length of train$= 150m$
Tunnel length$= 300m$
Time taken to cross the tunnel$= 40.5\sec$
So total distance covered by the train will be length of train and length of that tunnel
Total distance covered by train$= 150 + 300 = 450m$
Speed of the train using speed formula is given as,
Speed of train$= \dfrac{{{\text{total distance covered by train}}}}{{{\text{total time taken}}}}$
$= \dfrac{{450}}{{40.5}} = 11.11m/s$
In the question we have asked speed in$km/hr$, so using conversion formula we have
$1m/s = \dfrac{{18}}{5}km/hr$
Then we have,
$11.11m/s = \dfrac{{18}}{5} \times 11.11km/hr \\ = 39.996km/hr \sim 40km/hr \\$
So the speed in$km/hr$ is given $40km/hr$

So, the correct answer is “Option A”.

Note: Students can make mistakes in conversion of units. So we need to remember the unit conversion formula for speed from $m/s$to $km/hr$which is given as$1m/s = \dfrac{{18}}{5}km/hr$. Don’t confuse between distance and displacement of the object.