Question

A car covers a distance of 250km from Delhi to Jaipur in 5 hours and returns to Delhi covering the same distance in $5$ hours. What is the average velocity of the car for the whole journey?
$A.$ $25{\text{ }}km/hr$
$B.$ $50{\text{ }}km/hr$
$C.$ $0\;km/hr$
$D.$ $100{\text{ }}km/hr$

Answer 1

The ratio of total time and the displacement for the motion is called the average velocity. The displacement of an object is defined by the distance between its initial position and its final position.
To calculate the displacement or the velocity of an object the path of a whole journey does not need. It’s only related to the final and initial positions. This conception is also applicable for average velocity.

Formula used:
The average velocity of the car, $v = \dfrac{{{\text{total displacement(}}s{\text{)}}}}{{{\text{total time(}}t{\text{)}}}}$

Complete step by step answer: The velocity is the rate of change of displacement or the position change of an object with time.
And, The average velocity is the ratio of total displacement and the total time for a motion.
The displacement of an object is defined by the distance between its initial position and its final position. Hence,
To calculate the displacement or the velocity of an object the path of a whole journey does not need. It’s only related to the final and initial positions.
The average velocity of the car, $v = \dfrac{{{\text{total displacement(}}s{\text{)}}}}{{{\text{total time(}}t{\text{)}}}}$
In this problem, the car starts from Delhi and covers $250{\text{ }}km$ to reach Jaipur $5$ hours. The car returns to delhi through the same path of $250{\text{ }}km$in $5$ hours.
Hence the total displacement, $s$ = final position – initial position = $0$ .
$\therefore v = \dfrac{0}{{5 + 5}} = 0$.

Hence the average for velocity of the car is $0\;km/hr$.

Note: Carefully observe the question of what is needed there – speed or velocity.
Speed is the ratio of the distance of the whole path with time. And the average speed is defined as the ratio of the total path across the whole journey and the total time taken for covering the path.
So, for the above problem the Average Speed of the car = $\dfrac{{{\text{total path distance}}}}{{{\text{total time taken}}}} = \dfrac{{250 + 250}}{{5 + 5}} = 50km/hr$
But the velocity is related to the displacement of the car which becomes zero due to the initial and final position becoming the same for this journey. Hence the velocity also becomes zero.