Question

A train \[125m\] long passes a man run at \[5km/hr\] in the same direction in which the train is going in \[10\sec \]. Find the speed of the train.

Answer 1

Hint: In this question, distance and time is given. By using the speed formula, firstly we will find speed. After calculating the speed, we can calculate the value of relative velocity.

Complete step by step answer:
Speed of the train relative to the man\[{\text{ = }}\dfrac{{{\text{Distance}}}}{{{\text{Time}}}}\]
Distance and time are given in the question.
Distance=\[125m\]
Time=\[10\sec \]
Substitute the value of distance and tie and calculate the value of speed.
We get-\[\left( {\dfrac{{125}}{{10}}} \right)m/\sec \]
\[ Speed = \dfrac{{25}}{2}m/\sec \]
Convert the value of speed in \[km/hr\]
\[\Rightarrow \left( {\dfrac{{25}}{2} \times \dfrac{{18}}{5}} \right)km/hr\]
\[\Rightarrow Speed = 45km/hr\]
Let the speed of the train is x \[km/hr\] . so, the relative speed is=\[(x - 5)km/hr\]
\[\Rightarrow x - 5 = 45\]
\[\Rightarrow x = 50km/hr\]

So, the train is moving with \[50 km/hr\].

Note: Relative speed is the speed of a moving body with respect to another. It is a scalar quantity. Relative velocity is defined as the velocity of an object in the rest frame of another object. It is a vector quantity.
When two bodies are moving in the same direction then the relative speed is calculated by their difference and when two bodies are moving in opposite directions then the relative speed can be calculated by adding the speed of both bodies.