Question

A train 120 m long is running at a speed of 50 km/h. Find the time taken by it to cross a bridge 130 m long ?
please give step by step explanation. Ans is 18 sec​.

Answer 1

Given :-

A train of length 120 meters long is running at a speed of 50 km/hr .

Length of bridge = 130 long

Required to find :-

• Time taken to cross the bridge

Formula used :-

$\huge{\dagger{\boxed{\rm{ Time = \dfrac{ Distance }{ Speed }}}}}$

Units Conversion :-

In order to solve this question we need to convert the units of one physical quantity from one unit to another

The physical quantity whose units needed is " Distance "

Here convert the distance from meters to kilometres .

To convert it just divide it by 1000

So,

we know that

$\tt{ 1 \; meter = \dfrac{1}{1000} \; kilometers}$

Similarly,

120 meters = ? kilometres

$\Rightarrow{\tt{ \dfrac{120}{1000} = 0.12 \; kilometers }}$

130 meters = ? kilometres

$\Rightarrow{\tt{ \dfrac{130}{1000} = 0.13 \; kilometres }}$

Thus , units Conversion is done .

Solution :-

Given that :-

A train of length 0.12 km long is running at a speed of 50 km/hr .

Length of bridge = 0.13 km long

From the above we can conclude that

Length of the train = 0.12 km

Length of the bridge = 0.13 km

Total distance needed to be covered = 0.12 + 0.13

=> 0.25 kilometres

Similarly,

It is also mentioned that ,

Speed of the train is 50 km/hr

We need to find the time taken by the train to cross the bridge .

Here ,we have to use the familiar formula

That is ,

$\huge{\dagger{\boxed{\rm{ Time = \dfrac{ Distance }{ Speed }}}}}$

Here, substitute the required values

So, we get

$\longrightarrow{\tt{ Time = \dfrac{0.25 }{50 }}}$

$\longrightarrow{\tt{ Time = \dfrac{ 25 }{5000 }}}$

$\longrightarrow{\tt{ Time = 0.005 \; hours }}$

Here let's convert this hours into seconds for the factor of simplicity .

Hence,

Multiply it with 3600

This is because

Since ,

1 hours = 60 minutes

But

1 minute = 60 seconds

60 minutes = 60 x 60

=> 3,600 seconds

So,

Time = 0.005 x 3600

Time = 18 seconds

$\leadsto{\boxed{\small{\therefore{\tt{ Time\;taken\; by \; the \; train \; to \; cross \; the \; bridge \; = \; 18 \; seconds }}}}}{\bigstar}$