Question

A train crosses a pole in 15 second and a platform 100 metres long in 25 seconds, its length (in metres) is

Answer 1

❏ Formula Used

$\longrightarrow\sf\boxed{Velocity=\frac{Distance}{Time}}$

$\longrightarrow\sf\boxed{Acceleration=\frac{Velocity}{Time}}$

❏ Solution:-

Q)

A train crosses a pole in 15 second and a platform 100 metres long in 25 seconds, its length (in metres) is?

Ans)

Let, the length of the train is =L metre

and , the velocity of the train is = V m/sec

☞1st condition

The Train crosses a pole in 15 second;

it means the train crossed his length in 15 seconds.

$\therefore\sf time =\frac{distance}{velocity}$

$\sf\longrightarrow 15=\frac{L}{V}$

$\sf\longrightarrow \boxed{V=\frac{L}{15}}.............(i)$

☞2nd condition

train crosses a platform 100 metres long in 25 seconds,

it means it crossed the platform as well as it's length .

$\therefore time =\frac{distance}{velocity}$

$\sf\longrightarrow 25=\frac{L+100}{V}$

$\sf\longrightarrow \boxed{V=\frac{L+100}{25}}.........(ii)$

$\therefore comparing\: equ{}^{n}\:(i)\: and\: (ii), \:we \:get:$

$\sf\longrightarrow \frac{L}{15}=\frac{L+100}{25}$

$\sf\longrightarrow 25L=15(L+100)$

$\sf\longrightarrow 25L=15L+1500$

$\sf\longrightarrow 25L-15L=1500$

$\sf\longrightarrow 10L=1500$

$\sf\longrightarrow L=\frac{\cancel{1500}}{\cancel{10}}$

$\sf\longrightarrow \boxed{L=150\:metre}$

$\therefore \bf Length\: of \:the\: Train=150\:metre$

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