Question

A train of thousand meter long is moving with a velocity of 54km/hr. find the time it takes to cross the bridge of 2km long​

Answer 1

$\huge\mathcal\green{\underline{Given:-}}$

$\mathrm{Length \:of \:the\: train\: = 1000\:m}$

$\mathrm{Velocity \:of \:the \: train \:= 54 \:kmh}$

$\mathrm{Length \:of \:the\: bridge= 2\:km= 2\times{10^{3}m}=2000\:m}$

$\huge\mathcal\blue{\underline{To Find:-}}$

$\mathrm{The\: Time\: the \:train\: takes\: to\: cross\: the \:bridge\: of\: 2km.\:}$

$\huge\mathcal\purple{\underline{Sollution:-}}$

$\mathrm{Distance= Length \:of\: bridge+Length\: of \:Train}$

$\mathrm{Distance= 2000m + 1000m}$

$\mathrm\red{\underline{{Distance= 3000m}}}$

$\mathrm{Given \:that \:velocity \:of\: the \:train \:= 54\:kmh\:}$

$\mathrm{train \: speed = 54\times \frac{1000}{3600}}$

$\mathrm{train \: speed = 54\times \frac{10}{36}}$

$\mathrm{train \: spead = 54 \times 0.2777777778}$

$\mathrm\red{\underline{train \: speed = 15m {s}^{ - 1}}}$

$\mathrm\blue{Now,}$

$\mathrm{time \: = \frac{distance \: traveled}{speed \: of \: train}}$

$\mathrm{time = \frac{3000}{15} }$

$\mathrm\green{\underline{time = 200 \: seconds}}$

$\large\mathcal\red{\underline{\overline{\mid{\blue{Answer}}\mid}}}$

$\mathrm\purple{\underline{Therefore,\: The \:train\: will \:take \:200\: seconds}}$

$\mathrm\purple{\underline{ to \: cross\: the\: bridge.\:}}$

Answer 2

Heya!

In these kind of questions we have given with velocity, length of train, length of bridge.

Step 1) we should add the length of train and bridge. it gives the total distance covered by the train.

Step 2)we know that the velocity is always represented in s.i units i.e m/s. so we should convert km/he into m/s.

step 3) For finding out the time taken by the train to cross the bridge we should divide the total distance travelled by train by the speed of train.

Now let's get start to solve the given problem.

GIVEN:-

• Length of train= 1000m.
• Length of bridge= 2km= 2000m.
• Velocity of train= 54km/hour.

TO FIND:-

• The time taken by the train to cross the bridge of 2km.

SOLLUTION:-

Step 1)

DISTANCE TRAVELLED:-

Train legth+ Bridge length

= 1000m + 2000m = 3000m.

Here, we got the total distance travelled by train to be equal to 3000m.

Step 2)

They have given that the velocity of train is 54km/hr.

Let's convert km/hour to m/s.

⟹$\mathrm{54 \times \frac{1000}{60 \times 60}}$

⟹$54 \times \frac{1000}{3600}$

⟹$54 \times 0.2777777778$

⟹$15 \: m {s}^{ - 1}$

Here we got The speed of train as 15m/s.

Step 3)

TIME TAKEN= DISTANCE COVERED/ TRAIN SPEED.

TRAIN SPEED :-

⟹$\frac{3000}{15}$

⟹$200 \: sec$

HENCE, THE TRAIN WILL TAKE 200 SECONDS TO CROSS THE BRIDGE.

______________________________

⚕️For Diagram Refer The above answer @VILLAIN

Knowledge Booster:-

• The value of k = 1000, eg: 1k = 1x100= 1000.
• S.I unit of speed, velocity= m/s.
• Speed= Total distance covered/ Time taken.
• 1 hour= 60 min= 60 seconds x 60seconds.

Now you can answer any kind of questions of this pattern.

Happy learning!

Brainly Team.