Question

A train is passing through a platform of
length 50 m with uniform velocity. It takes
15s to cross the platform and 5 s to cross a
man standing on a platform. Mark the correct
option(s).
(a) The length of train is 25 m
(b) The length of train is 50 m
(c) The speed of train is 10 ms
(d) The speed of train is 5 ms​

Answer 1

Answer:

(d) The speed of train is 5 ms​

Explanation:

Let v be the velocity of the train, and l be its’ length. Then:  

(l+50)m/15s=v and  

l m/5 s=v

So:

l=5v

l+50=15v

3l=l+50

2l=50

l=25 m

v=75/15=5 m/s

Answer 2

Answer:

Option (a) The length of train is 25 m and option (d) The speed of train is $5\frac{m}{s}$. is correct.

Concept:

To calculate the speed if distance and time is given.

$Speed = \frac{Distance}{Time}$

Given:

Length of platform = 50 m

Time taken by train to cross the platform = 15 s

Time taken by train to cross the man = 5 s

Find:

We have to find the length of train.

Solution:

Let the length of train be l and velocity of train be v.

So, speed of train = $\frac{length of train + length of platform}{time taken by train to cross the platform}$

S  = $\frac{L+ 50}{15} .. (1)$

Again, speed of train = $\frac{length of train}{time taken by train to cross the man}$

S = $\frac{L}{5} .. (2)$

Now, equate (1) and (2), we have:

$\frac{L + 50}{15} = \frac{L}{5}$

5 (L + 50) = 15 L

5L + 250 = 15L

10L = 250

L = 25 m

$Speed of train = \frac{length of platform + length of train }{time taken} \\V = \frac{50 + 25}{15} \\V = \frac{75}{15} \\V = 5 \frac{m}{s}$

Hence, length of the train is 25 m and speed of train is $5\frac{m}{s}$.

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