Question

A $ 200m $ long train crosses a $ 400m $ long bridge with a speed of $ 36km.{h^{ - 1}} $ . Calculate the time taken by the train to cross the bridge.

Answer 1

Hint: A fast-moving object travels quickly and covers a wide distance in a short period of time, while a slow-moving object travels slowly and covers a limited distance in the same amount of time.

Complete step-by-step answer:
We have to find the time taken by the train to cross the bridge. From the question, we already have the values of the speed of the train, the length of the bridge, and the length of the train. Using these given values, we can calculate the time taken by the train to cross the bridge.
The speed of the train is equal to $ 36km.{h^{ - 1}} $ .
Speed $ = 36km.{h^{ - 1}} $
We have to convert the unit of speed into the standard unit which is $ m{s^{ - 1}} $ . To convert the unit, we have to divide the given speed with $ 3.6 $
Speed $ = \dfrac{{36}}{{3.6}} = 10m{s^{ - 1}} $
Now, we have to calculate the total distance travelled to cross the bridge. The total distance travelled to cross the bridge is equivalent to the sum of the length of the bridge and the length of the train.
Total distance travelled to cross the bridge $ = 200m + 400m = 600m $
The rate at which an object travels over a given distance is known as speed.
We know the formula of speed is $ speed = \dfrac{{dis\tan ce}}{{time}} $
On rearranging the terms in the above formula, we get
 $
  time = \dfrac{{dis\tan ce}}{{speed}} \\
   = \dfrac{{600m}}{{10m{s^{ - 1}}}} \;
   = 60s \;
  $
We know that $ 60 $ sec is equal to $ 1 $ minute.
Therefore, the time consumed by the train to cross the bridge is equal to $ 1 $ min.
So, the correct answer is “ $ 1 $ min”.

Note: Speed is the rate at which an object moves along a path in terms of distance, while velocity is the rate and direction of travel. In other words, speed is a scalar value, while velocity is a vector value.