Question

A 150 m long train is moving with a uniform velocity of 45km/h. The time taken by the train to cross a bridge of length 850 meters is ________

Answer 1

Hint:
In this problem we have to find the time taken by the train to cross a bridge of length 850 meters. We can take the train by crossing a bridge, the distance travelled by the train is the sum of the length of the bridge and the length of the train. Then by using the velocity formula to calculate the time by hours. We convert it to seconds, because the unit mentioned in the problem is meter. Hence, we have to convert it into seconds.

Complete step-by-step answer:
It is given that,
The length of the train is 150 meters.
The length of the bridge is 850 meters.
Since while crossing a bridge, the distance travelled by the train is the sum of the length of the bridge and the length of the train.
So the distance travelled by the train is = 150m+850m
=1000m
Also given that the train is moving with a uniform velocity of 45km/h.
The formula for velocity is given by
Velocity = Displacement/Time.
The train is moving with a uniform velocity of 45km/h means the train is moving 45km in 1 hour.
The relation between km/hour and m/sec is
1km/hour=
$
  \dfrac{{1000}}{{3600}}m/\sec \\
   = \dfrac{5}{{18}}m/\sec \\
$
Then 45km/hour =\[\dfrac{5}{{18}} \times 45 = \dfrac{{25}}{2}m/\sec \]
Thus the train is moving \[\dfrac{{25}}{2}m\]in 1 second
The train is moving 1m in \[\dfrac{1}{{\dfrac{{25}}{2}}}\] second
The train is moving 1000m in \[\dfrac{1}{{\dfrac{{25}}{2}}} \times 1000\] second
$
   = 1 \times \dfrac{2}{{25}} \times 1000\sec \\
   = 2 \times 40\sec \\
   = 80 sec
$
Hence, the time taken by the train to cross a bridge of length 850 meters is 80 seconds.

Note:
If a body travels equal distances in an equal interval of time along a particular direction, the body is said to be moving with a uniform velocity. Here we make mistakes on converting unit kilometers to meters. Usually we measure the velocity by kilometer per hour. In this problem the distance is measured by meter. Here we will forget to convert the unit.