Question

A train takes 9seconds to cross a pole .If the speed of the train is 48 km/hr.The lenth of the train is

Answer 1

$\underline{\underline{\Huge{\textbf{Question:}}}}$

A train takes 9seconds to cross a pole. If the speed of the train is 48 km/hr.The lenth of the train is _________

$\underline{\underline{\Huge{\textbf{Solution:}}}}$

$\sf\textsf{Given,}\\ \sf\textsf{Speed of the train = 48 kmph}$
$\sf\textsf{time taken by the train to cross a pole = 9 sec}\\ \sf\textsf{Length of the train = ?}$



$\underline{\Large{\textsf{Step-1:}}}$
$\textsf{Express the Speed of the train in mps}$

$\bigstar\: \: \boxed{\displaystyle\large{\mathbf{1\: kmph\: =\: \dfrac{5}{18}\: mps}}}$

$\implies \sf\textsf{48 kmph = 48 \times \dfrac{5}{18} mps}$

$\implies \sf\textsf{48 kmph = \dfrac{40}{18} mps}$

$\therefore \sf\textsf{The Speed of the train = \dfrac{40}{3} mps}$



$\underline{\Large{\textsf{Step-2:}}}$
$\textsf{Find the distance covered by the train in 9 seconds}$

$\sf\textsf{We have,}$

$\bigstar\: \: \boxed{\displaystyle\large{\mathbf{Speed \: =\: \dfrac{Distance\: covered}{time\: taken}}}}$

$\implies \large{\sf\textsf{Distance Covered = Speed \times time taken}}$

$\sf\textsf{Plug in Values}$

$\implies \sf\textsf{Distance Covered = \dfrac{40}{3}\times 9}$

$\implies \sf\textsf{Distance Covered = 40 \times 3}$

$\implies \sf\textsf{Distance Covered = 120 m}$



$\underline{\Large{\textsf{Step-3:}}}$
$\textsf{Find the length of the train}$

$\sf\textsf{If the width of the pole is assumed, to be negligible}\\\sf\textsf{Length of the train is equal to the distance covered}\\\sf\textsf{by the train in crossing the pole}$

$\bigstar\: \: \boxed{\large{\textbf{Length of the train = Distance Covered by the train}}}$



$\therefore$
$\blacksquare\: \: \textsf{The Length of the train is \underline{\Large{\textbf{120 m}}}}$