Question

A train 200 meters long is running with a speed of 36 kmph. How much time will it take to pass standing police?

Answer 1

Hint: In this question, we need to find the time taken by the train to travel the given distance which can be found by using the formula which gives the relation between speed, distance and time given by \[v=\dfrac{d}{t}\]. Here, we need to convert the given speed into meters per second using the conversion given by \[1kmph=\dfrac{5}{18}m/s\].

Complete step by step solution:
Let us assume that the speed of the train as v, distance travelled by train as d and the time taken to travel the given distance as t.
As we already know that the relation between the speed of an object, distance travelled by it and the time taken to travel the given distance is given by the formula
\[v=\dfrac{d}{t}\]
Now, we need to convert the given speed of the train in kmph to meter per second as the distance travelled by it is given in the meters.
Here, we already know that the relation between kmph and meter per second is given by
\[1kmph=\dfrac{5}{18}m/s\]
Now, the given speed of the train in the question is
\[\Rightarrow 36kmph=36\times \dfrac{5}{18}m/s\]
Now, on cancelling the common terms and simplifying further we get,
\[\Rightarrow 36kmph=2\times 5m/s\]
Now, on simplifying this further we get,
\[\Rightarrow 36kmph=10m/s\]
Now, from the given values in the question we have
\[v=10,d=200\]
Now, the relation is given by the formula
\[\Rightarrow v=\dfrac{d}{t}\]
Now, on further substituting the respective values we get,
\[\Rightarrow 10=\dfrac{200}{t}\]
Now, on rearranging the terms we get,
\[\Rightarrow t=\dfrac{200}{10}\]
Now, on further simplification we get,
\[\therefore t=20s\]
Hence, the train takes 20 seconds to pass a standing police.

Note:
Instead of using the relation between speed, distance and time we can also solve this question by considering that if the train travels 36 km in 1 hour how much time will it take to travel 200 meters which on further simplification gives the result.
It is important to note that before substituting the given values in the formula we need to first convert them accordingly into the same unit system and then simplify. Because if we calculate without converting into the same units then we cannot comment on the unit of the obtained result which will be incorrect.