Question

A train having a length of 375 m travels at a speed of 45 km/h. How long will it take to pass a signal post?

Answer 1

Hint: In this question, it is given that the length of the train is 375 m. One important thing you have to note here in this question is that when the length of the train is given then we will consider it as distance covered by the train. A train is not a point object so we cannot ignore the length of the train. Now, the train travels at the speed of 45 km/h. It means first we will convert the speed of km/h into m/sec. After that we will find what time will take to pass a signal post. So, students, we will use the formula $ Time = \dfrac{{Dis\tan ce}}{{Speed}} $ to solve this question.

Complete step-by-step answer:
GIVEN
The train travels at the speed of 45 km/h. It means first we will convert the speed of km/h into m/sec. After that we will find what time will take to pass a signal post. So, students, we will use the formula $ Time = \dfrac{{Dis\tan ce}}{{Speed}} $ to solve this question.
Distance to be travelled to pass a signal post = 375m
Speed of train
= 45 km/h [ convert into m
= $ \dfrac{{45 \times 1000\,m}}{{60 \times 60\,\sec }} = \dfrac{{450}}{{36}} = \dfrac{{25}}{2}\, $ m/sec
As we know that,
$ Speed = \dfrac{{Dis\tan ce}}{{Time}} $
$ \Rightarrow Time = \dfrac{{Dis\tan ce}}{{Speed}} $
Putting the value of distance and Speed in the above formula.
Time = $ \dfrac{{375}}{{\dfrac{{25}}{2}}} = \dfrac{{375}}{{25}} \times 2 = 30 $ seconds
Hence, the train will take 30 seconds to cross the signal post.

Note: As we know that, there are 1000 m = 1 km and 1 hour = 60 min = 60 x 60 sec. We will consider the length of the train as the distance covered by the train. That is why we have taken 375 m in place of distance. But if there were a car or a bus then we will ignore their length because car or bus is counted as a point object. One more thing you have to make sure that the unit of the values must be the same; if distance is given in meters then speed must be in meters per second (m/sec) or vice-versa.