Question

A train 100 m long is moving with the speed of $40\dfrac{{km}}{{hr}}$. A person is moving in that direction at a speed of $4\dfrac{{km}}{{hr}}$. What time is it taken by train to cross a person?

Answer 1

Train and a person are moving in the same direction. We will find the relative speed of a train with respect to a person. We will calculate time taken to cross a person using $speed = \,\dfrac{{dis\tan ce}}{{time}}$ formula.

Complete step by step answer:
Speed:
Distance travelled by an object per unit time is known as speed.
Distance time formula;
$speed = \,\dfrac{{dis\tan ce}}{{time}}$ … (1)
S.I. unit of speed is $\dfrac{m}{{\sec }}$.
Relative speed:
When two or more than two objects are in motion, then the term ‘relative’ is used. It is used to compare physical quantities between the objects. Similarly, relative speed is defined as speed of one object with respect to another object in motion.
Speed of train $= 40\dfrac{{km}}{{hr}}$
Speed of person in motion $= 4\dfrac{{km}}{{hr}}$
Person is moving in the direction of the moving train. Relative speed of train with respect to person will be
$= 40\dfrac{{km}}{{hr}} - 4\dfrac{{km}}{{hr}}$
$= 36\dfrac{{km}}{{hr}}$
$= 36 \times \dfrac{{1000}}{{60}}\dfrac{m}{{\sec }}$
$= 600\dfrac{m}{{\sec }}$
Length of train is 100 m
Time taken by train to cross person $= \dfrac{{dis\tan ce\,\,travelled}}{{relative\,\,speed\,}}$
$Time\,\, = \,\dfrac{{100}}{{600}}\,\,\sec$
$\Rightarrow Time = 0.166s$

Therefore, time taken by train to cross a person is 0.166 seconds.

Note:
If the relative speed of a person with respect to a train is taken then speed would have been negative. This negative sign indicates the opposite direction.
Secondly, if speed given in terms of $\dfrac{{km}}{{hr}}$ is not converted to $\dfrac{m}{{\sec }}$, then this might alter results and we will get a wrong solution.