Question

A car travels distance S on a straight road in two hours and then returns to the straight point in the next three hours. Its average velocity is:
A. $S/5$
B. $2S/5$
C. $S/2 + S/3$
D. $Zero$

Answer 1

Hint:We need to find the average displacement of a car when it travels a distance S and returns to its starting point. Time taken by the vehicle for covering a distance S and return to its starting point is given. We know that average velocity is the ratio of total displacement to total time taken. By calculating total displacement and real-time, we get the average velocity of the car.

Complete step by step answer:
We have a car that travels a distance S on a straight road. The time taken to travel S distance is given to be 2 hours.After traveling A distance, the car returns to the starting point.
Therefore, the total displacement traveled by car will become,
$\begin{array}{l}
{S_{net}} = S + \left( { - S} \right)\\
 = 0
\end{array}$
Here ${S_{net}}$ is the net displacement.
The time taken by the car to return to the initial point is given as 3 hours. Hence the total time becomes 5 hours.
We are asked to calculate the average velocity of the car. We know that the equation can calculate average velocity,
$\overline V = \dfrac{{{S_{net}}}}{T}$
Here, T is the total time, equal to 5 hours, and $\overline V $ is the average velocity.
We will now substitute, ${S_{net}} = 0$ and T=5 hrs to find the value of $\overline V $.
$\begin{array}{l}
\overline V = \dfrac{{0\;}}{{5\;{\rm{hr}}}}\\
 = 0
\end{array}$
Therefore, the average velocity is zero, and the correct option is (D).
Option (A), (B), (C) has some numeral values which are incorrect.

Note:Here, we are calculating the average velocity of the car. Therefore, we consider the total displacement traveled by car, not the entire distance of the vehicle. We know that the total displacement of the vehicle is zero because the car returns to its starting. But the total distance traveled by car is not zero, and it is equal to 2S.