Question
Question: A train is running at a speed of \(40\,km{\kern 1pt} h{r^{ - 1}}\) and it crosses a post in \(18\sec...
A train is running at a speed of 40kmhr−1 and it crosses a post in 18sec. What is the length of the train?
Solution
In order to solve this question we need to understand the distance, displacement and velocity of particles. So distance is defined as a physical quantity which is equal to path length covered by a particle, it is scalar quantity. Displacement is defined as the shortest path length between initial and final points of a particle motion, it is a vector quantity. Speed is defined as distance covered by particle per unit time, it is a scalar quantity.Velocity is defined as displacement covered by particle per unit time, it is a vector quantity.
Complete step by step answer:
Speed of the train is given as, v=40kmhr−1. We have to convert the train speed in msec−1 so to do the same, speed in msec−1 is,
v=40×185msec−1
since 1Kmhr−1=185ms−1
⇒v=11.11msec−1
Time taken by train to cross a post is, t=18sec
Let the length of the train be “L”.So to cover the post, the whole length of the train must go past by post. So from the definition of speed we get, v=td.So the distance or length of train covered is, d=vt.Putting values we get,
L=(11.11msec−1)×(18sec)
∴L=200m
Therefore the length of train is, L=200m.
Note: It should be remembered that, here we have assumed that the motion is analyzed from a static frame of reference or inertial frame of reference in which the observer is assumed to be at rest. If the motion is analyzed from an observer which is also moving with respect to the train, then in that case we have to relatively add or subtract velocity (depending on direction) to get the final result.