Question

A train $140\;{\rm{m}}$ long, passes a telegraph post in ${\rm{14}}\;{\rm{sec}}$. Find time taken by it to pass a platform $160\;{\rm{m}}$ long.

Answer 1

In the solution, first we have to find the speed of the train by using the formula, ${\rm{speed}} = \dfrac{{{\rm{distance}}}}{{{\rm{time}}}}$. After that we have to calculate the total distance by adding the length of the train and the length of the platform. Once we get the speed and the total distance and speed we have to calculate the time taken by the train by using the formula,
${\rm{time}} = \dfrac{{{\rm{distance}}}}{{{\rm{speed}}}}$.

Complete step by step answer:
Given, length of the train $= 140\;{\rm{m}}$
Time taken by the train to cross a telegraph post ${\rm{ = 14}}\;{\rm{sec}}$
Length of the platform $= 160\;{\rm{m}}$
Step I: Now, to find the speed of the train,
We know that,
${\rm{speed}} = \dfrac{{{\rm{distance}}}}{{{\rm{time}}}}$
Therefore, the speed of the train,
$\begin{array}{c}{\rm{speed}} = \dfrac{{{\rm{140}}\;{\rm{m}}}}{{{\rm{14}}\;{\rm{sec}}}}\\\ = 10\;{\rm{m/sec}}\end{array}$
Step II: Distance of platform$= 160\;{\rm{m}}$
Hence, the total distance
$\begin{array}{c} = 140 + 160\;{\rm{m}}\\\ = 300\;{\rm{m}}\end{array}$
Step III: Now, we need to find the time taken by the train to cross the platform.
We know that,
${\rm{time}} = \dfrac{{{\rm{distance}}}}{{{\rm{speed}}}}$
Therefore, time taken by the train to cross the platform is
$\begin{array}{c} = \dfrac{{{\rm{300}}}}{{{\rm{10}}}}\\\ = 30\;\sec \end{array}$

Hence, the required time is $30\;\sec$.

Note: Speed of an object is the total distance covered at a particular time. Here we have to find the time taken by the train to pass a platform of $160\;{\rm{m}}$ long. In step I, find the speed of the train. Speed = The rate at which someone or something moves. Formula for speed is, ${\rm{speed}} = \dfrac{{{\rm{distance}}}}{{{\rm{time}}}}$. In step II, find the total distance. In step III, find the time taken by the train to cross the platform. Time: a point of time as measured in hours and minutes past midnight or noon. Formula for time taken is, ${\rm{time}} = \dfrac{{{\rm{distance}}}}{{{\rm{speed}}}}$. An object's velocity is the rate of change in its location toward a reference point, which is a function of time. Velocity is the equivalent of determining the speed and direction of travel of an object.