Question

A car starts from Bengaluru, goes 50 km in a straight line towards south, immediately turns around and returns to Bengaluru. The time taken for this round trip is 2 hours. The magnitude of the average velocity of the car for this round trip
A) is 0
B) is 50 km/hr
C) is 25 km/hr
D) cannot be calculated without knowing acceleration.

Answer 1

Hint: To calculate the magnitude of average velocity, we require displacement (difference between the distances) and the time, which are already given, so we just need to substitute these values in the formula of average velocity given as:
 $ velocity({V_{av}}) = \dfrac{{displacement}}{{time}} $

Complete step-by-step answer:
The distance covered in one side $ \left( {{D_1}} \right) $ = 50 km
The distance covered in returning $ \left( {{D_2}} \right) $ = 50 km
Displacement (D) is given by the difference between the two distances
D = $ {D_1} - {D_2} $
Substituting the values, we get:
D = (50 – 50) km
D = 0 km
Now, the average velocity is defined as the displacement of an object per unit time:
 $\Rightarrow velocity({V_{av}}) = \dfrac{{displacement}}{{time}} $
Given time = 2 hours
So, the value of average velocity is:
  $
\Rightarrow {V_{av}} = \dfrac{0}{2} \\
\Rightarrow {V_{av}} = 0 \\
  $
Therefore, the average velocity of the car for this round trip is 0 and the correct option is A).
OR
Given:
Initial position of the car = Final position of the car (Bengaluru)
When this is the case the displacement is always equal to 0.
And average velocity is:
 $ velocity({V_{av}}) = \dfrac{{displacement}}{{time}} $
When displacement is 0, the average velocity will also be 0.

So, the correct answer is “Option A”.
Note: Acceleration depends upon velocity as it is velocity per unit time, but the velocity does not depend upon the acceleration but depends upon the displacement of the object, hence the last option cancels out.
Remember: If the object starts and finishes its motion at the same place, its displacement will always be equal to zero.