Question

Sumith was waiting on a $200m$ long railway platform when he saw a train travelling at a speed of $54km{h^{ - 1}}$ . If the train took $50s$ to pass the platform, what is the length of the train $\left( {{\text{in metre}}} \right)$?

Answer 1

Hint: Velocity: the rate of change of displacement with respect to time is called velocity. It is a vector quantity and it’s S.I. unit is $m{s^{ - 1}}$ .
Displacement: Change is position of object from fixed point with time. It’s S.I. unit is $m$ . Distance will always be positive.
Formula used:
 $v$ $ = $ $\dfrac{d}{t}$
Where $d$ is the displacement and $t$ is time taken.
To convert $km{h^{ - 1}}$ to $m{s^{ - 1}}$ should multiply it with $\dfrac{5}{{18}}$ .

Complete Step by step solution:
As, given in question,
The length of railway platform, $l = 200m$
Speed of train,$v$ = $54km{h^{ - 1}}$
$ \Rightarrow v = 54 \times \dfrac{5}{{18}}m{s^{ - 1}}$
The length of train is denoted by$s$
Time taken to cross the station,\[\;t = 50s\;\]
The total distance travelled by train $ = l + s$
By using formula,
 $
   \Rightarrow v = \dfrac{{l + s}}{t} \\
   \Rightarrow 15m{s^{ - 1}} = \dfrac{{200 + s}}{{50}} \\
   \Rightarrow s = 550m \\
$
Hence, the length of the train will be $550m$ .

Additional Information:
Velocity can be distinguished from speed as velocity gives the magnitude and direction of a body whereas speed gives us only the magnitude of the body.
Speed is a scalar quantity whereas velocity is a vector quantity.
Speed can never be negative whereas velocity can be positive, negative or zero.

Note
 Initial velocity is the velocity of the object with which it has started moving and final velocity is the terminal velocity of the object.
Angular velocity is defined as the rate of change of angular displacement with time. For example, it is used to measure the rotation of a body with respect to the inertial frame of reference.