Question

Please tell me about the direct and in verse variation ques.
Q. A train 280 m long is running at a speed of 42 km/he. How much time will it take to pass a mam standing on a platform

Answer 1

Given :-

▪ A train 280 m long is running at a speed of 42km/h.

To Find :-

▪ Time taken by the train to pass a mam standing on a platform.

Solution :-

The length of mam is almost negligible compared to the train. So, We would take the position of mam as a point object and we would have to find the time taken by the train to pass that point object and that will be our answer.

First of all, The train will have to travel a distance which is equal to its length and the time taken by the train to cover its length is the actual time taken to pass mam.

We have,

• Speed = 42 km/hr
• Distance = 280 m

Now, Convert the units of speed into m and seconds.

⇒ Speed = 42 km/hr

⇒ Speed = 42 × 1000 / 3600 m/s

⇒ Speed = 420 / 36 m/s

⇒ Speed = 105/9 ms⁻¹

Now, Using the distance time formula, we have

⇒ Time taken = Distance / Speed

⇒ T = 280 / (105 / 9)

⇒ T = 2520 / 105

⇒ T = 24 seconds

Hence, The train will take 24 seconds to pass a mam standing on a platform.

Answer 2

Given:

• Length of train = 280m
• speed =42 km/hour

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Need to find :

• Time taken by the train to pass a man=?

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SOLUTION:

Speed of train is:

42km/hour

$= \dfrac{42 \times 1000m}{3600sec}$

$= \dfrac{42 \times 5 \: m}{18 \: sec}$

= $\dfrac{35}{3} m/s$

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Now to cross a man. The train only needs to travel it's length. The time taken for crossing the man starts from when the front part of the train crossed the man to the time when the end of train crossed the man.

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Thus

the train goes $\dfrac{35}{3} m$ in 1sec.

So, it'll travel 280m in:

$\dfrac{3}{35} \times 280sec$

$= 8 \times 3sec$

$\red{ = 24sec}$