Question

. A train 200 m long crosses a bridge 300 m long.
It enters the bridge with a speed of 30 ms 1 and
leaves it with a speed of 50 ms-1. What is the time
taken to cross the bridge ?
(1) 2.5 (2) 7.55 (3) 12.5 (4) 15.0s
To​

Answer 1

Answer:

A train 200m long crosses a bridge 300m long. It enters the bridge with a speed of 3ms

−1

and leaves it with a speed of 5ms

−1

. What is the time taken to cross the bridge?

HARD

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CALCULATOR

Enter the know values to find unknown

Acceleration

Distance

Final Velocity

v = u + a*t

Initial Velocity u

m/s

Final Velocity v

m/s

Time t

s

Acceleration a

m/s²

RESET VALUES

ANSWER

The acceleration is given as,

a=

2s

v

2

−u

2

=

2×500

(5)

2

−(3)

2

=

1000

16

m/s

2

The time taken to cross the bridge is given as,

t=

a

v−u

=

1000

16

5−3

=125s

Thus, the time taken to cross the bridge is 125s.

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Answer 2

Given:-

 

☞Length of train = 200m

☞Length of bridge = 300m

☞Initial speed of train = 30m/s

☞Final speed of train = 50m/s

   

To Find:-

 

☞Time Taken to cross the bridge -?

   

Formulas to be used:-

   

☞ $\boxed{\bf{v^2-u^2 = 2as}}$

☞  $\boxed{\bf{v- u= at}}$

where,

v= Final speed

u= initial speed

a= acceleration

t= time

s= distance covered

 

Solution:-

   

Total distance covered by the train = length of bridge + length of the train

                                                           = 200+100 = 500m

S= 500m

☞First Find acceleration [a] =>

By using 3rd equation of motion i.e,

$\sf{v^2-u^2 = 2as}$

Put given values in the formula,

$\sf{ \implies 50^2-30^2 = 2\times a\times 500}$

$\sf{\implies 2500- 900 = 1000 \times a}$

$\sf{ \implies a = \dfrac{1600}{1000} }$

$\sf{ \implies a= 1.6}$

Acceleration=1.6m/s²

       

     

Now,

☞We will find Time taken

By using 1st equation of motion, i.e.

$\sf{v- u= at}$

put  the given values in the formula,

$\bf{\implies 50-30 = 1.6 \times t}$

$\bf{\implies t= \dfrac{20}{1.6} }$

$\bf{\implies t= 12.5 }$

So, Option (3) is Correct.

   

Therefore, Time taken by train is 12.5 seconds.