Question

A train running at a speed of 54km/hr
passes a signal in the past 10 sec. Find the length of the train in metres ​

Answer 1

Given:-

• Speed of train ,s = 54km/h

• Time taken to cross a signal post ,t = 10 s

To Find:-

• Length of train , d

Solution:-

⠀⠀⠀⠀⠀⠀⠀⠀⠀According to the Question

we have to calculate the length of train . Firstly we convert the speed of train into m/s. So we multiply the given speed by 5/18 we get the speed into m/s.

$:\implies$ s = 54×5/18

$:\implies$ s = 3×5

$:\implies$ s = 15m/s

So , the speed of train is 15m/s .

Now, calculating the length of train . As we know that

• d = st

where,

• d denote length of train
• s denote speed
• t denote time taken to cross post

substitute the value we get

$:\implies$ d = 15×10

$:\implies$ d = 150m

• Hence, the Length of the train is 150m.

Answer 2

Given : A train running at a speed of 54 km/hr passes a signal in the post 10 sec.

Exigency To Find : The length of the train in metres .

⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀

⠀⠀⠀⠀⠀Given that ,

⠀⠀⠀⠀⠀⠀⠀▪︎⠀⠀The Speed ( s ) of train is 54 km/hr .

⠀⠀⠀⠀⠀⠀⠀▪︎⠀⠀Total time taken ( t ) to páss one signal post is 10 seconds .

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀Changing the unit of speed from km/hr to m/s :

$\qquad :\implies \sf Speed \:=\: 54 \: km/hr \:\:$

⠀⠀⠀As , We know that ,

⠀⠀⠀⠀⠀⠀⠀▪︎⠀⠀For changing the unit from km / hr to m/s we multiply the given by 5/18 .

$\qquad :\implies \sf Speed \:=\: 54 \: km/hr \:\:$

$\qquad :\implies \sf Speed \:=\: 54 \: \times \:\dfrac{5}{18} \:\:$

$\qquad :\implies \sf Speed \:=\:\cancel {54} \: \times \:\dfrac{5}{\cancel {18}} \:\:$

$\qquad :\implies \sf Speed \:=\: 3 \: \times \:5\:\:$

$\qquad :\implies \sf Speed \:=\: 15\:\:$

$\qquad \therefore \pmb{\underline{\purple{\frak{\: Speed\:\:(\:or\:s\:) \:=\: 15\:\:\:\:m/s \: }}} }\:\:\bigstar$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀☆ Finding Length of train :

$\dag\:\:\pmb{ As,\:We\:know\:that\::}\\\\\qquad\maltese\:\: \bf Formula\:for\:Distance\::\:$

$\qquad \dag\:\:\bigg\lgroup \pmb{ \frak{Distance \:(\:d\:)\:=\: Speed\:(\:s\:)\:\times \:Time \: Taken \:(\:t\:) }}\bigg\rgroup$

⠀⠀⠀⠀⠀Here Speed is 15 m/s & Time taken is 10 seconds

$\qquad \dashrightarrow \sf Distance \:(\:d\:)\:=\: Speed\:(\:s\:)\:\times \:Time \: Taken \:(\:t\:)$

⠀⠀⠀⠀⠀⠀$\underline {\boldsymbol{\star\:Now \: By \: Substituting \: the \: known \: Values \::}}$

$\qquad \dashrightarrow \sf Distance \:(\:d\:)\:=\:15\:\times \:10$

$\qquad \dashrightarrow \sf Distance \:(\:d\:)\:=\:150$

$\qquad \therefore \pmb{\underline{\purple{\frak{\: Distance \:\:(\:or\:d\:) \:=\: 150\:\:\:\:m \: }}} }\:\:\bigstar$

$\qquad \therefore \underline {\sf \:\:Hence ,\:The \:Length \:of \:train \: is \:\bf 150 \: m\:.\:}$