Question

How long will a train, running at a speed of $45\,Kmph$ cross a standing man, given the length of the train is $450\,m$ ?
A. $100\sec$
B. $150\sec$
C. $50\sec$
D. $36\sec$

Answer 1

In order to solve this question, we will use the general relation between speed, distance and time for a body. It’s related as $speed = \dfrac{\text{distance}}{\text{time}}$ and we will convert the given length and speed of the train in the same suitable units to calculate the time taken by train to cross a standing man.

Complete step by step answer:
Let us suppose a man standing somewhere at point says $A$ and the length of the train is given by $length = 450\,m$ , Let us first convert this length into $Km$ units.
Since, $1m = {10^{ - 3}}Km$ then,
$450\,m = 0.45\,Km$
Hence, the length of the given train is $0.45\,Km$

Speed of train is given as $45\,kmph$ which is read as Kilometre per hour. In order to cover the whole length of train passing by a man standing at point $A$ , this point must be covered as the total length of the train and with a speed of train.So, time taken by train to cross a standing man is given as:
$\text{speed} = \dfrac{\text{distance}}{\text{time}}$
$\Rightarrow \text{time} = \dfrac{{0.45}}{{45}}$
$\Rightarrow \text{time} = 0.01\,hour$
We can also convert the time in hours to seconds as;
One hours has $3600\sec$ , so
$\text{time} = 3600 \times 0.01$
$\therefore \text{time} = 36\sec$
Hence, time taken by train to cross standing man is $time = 36\sec$ .

So, the correct option is D.

Note: Since, the train was moving with uniform speed hence it has no acceleration and from one end of the train to the other end every part of the train was moving with the same speed. Remember the useful conversions of units like $1\,Km = 1000\,m$ and $1\,hour = 3600\sec$.