Question

A 150 m long train is moving with constant velocity of 12.5 m/s. Find
(i) the equation of the motion of the train, (ii) time taken to cross a pole.
(iii) The time taken to cross the bridge of length 850 m is?​

Answer 1

Time need to cross the pole by train = 12 second

Time need to cross the pole by train = 12 secondTime taken to cross the bridge of length of 850 m is 80 second

$\tt{Step-by-step\: explanation:}$

Data:

Distance = d = 150 m  

velocity = v = 12.5 m/s

Required:

1) Time take to cross the pole = t = ?

2) Time take to cross the bridge of length 850 m = t = ?

Calculation:

We know that

$\boxed{\tiny \sf\color{blue}{The \: velocity \: of \: body = \dfrac{Distance}{Time}}}$

Since train has to cross the pole so the distance cover by the train to cross the pole is equal to length of train

Putting values in the formula we get

$\rm{12.5 = \dfrac{150}{t}}$

$\rm{t = \dfrac{(150)}{12.5} = 12\: s}$

So time need to cross the pole by train = 12 second

And

When train has to cross the bridge of length 850 m then

Total distance = D = 150 m + 850 m = 1000 m

Putting the values we get

$\boxed{\small \sf\color{blue}{Velocity = \dfrac{Distance}{Time}}}$

$\sf{12.5 = \dfrac{1000}{t}}$

$\sf{t = \dfrac{1000}{12.5}  = 80\: s}$

• Hence, time taken to cross the bridge of length of 850 m is 80 second

Answer 2

Given:

Train : 150m

Velocity: 12.5m/s

Solution:

$\sf \: (i) Speed= \frac{distance}{time}$

$\sf 12.5 =\frac{y+150}{x}$

$\sf 12.5x=y+150$

Therefore, the motion of the train:

$\boxed{\tt \: y = 12.5x-150}$

(ii) Using the equation of motion of train,

$\boxed{\tt y = 12.5x-150}$

$\sf Speed=\frac{distance}{time}$

$\sf 12.5=\frac{y}{x}$

$\sf y=12.5x$

The train of length 150m should cross the pole is considered.

Sub. y=150

$\sf 150=12.5x$

$\sf x=12 seconds$

(iii) Using,

$\boxed{\tt y = 12.5x-150}$

$\sf y=850m$

$\sf 850=12.5x-150$

$\sf 850+150=12.5x$

$\boxed{\sf x=80sec}$