Question

A car travels from Bangalore to Mumbai and returns in $20hours$. What is the average velocity and average speed of the car if odometer reading of the car, when it started was $2200km$ and when finished was $3800km$?

• A. $\text{Average velocity = 0 kmph}$
  $\text{Average speed = 0 kmph}$
• B. $\text{Average velocity = 0 kmph}$
  $\text{Average speed = 80 kmph}$
• C. $\text{Average velocity = 80 kmph}$
  $\text{Average speed = 80 kmph}$
• D. $\text{Average velocity = 80 kmph}$
  $\text{Average speed = 0 kmph}$

Answer 1

The correct option is B $\text{Average velocity = 0 kmph}$

$\text{Average speed = 80 kmph}$
Given:
Finally, the car returns to the original position
Initial odometer reading, $r_1=2200km$
Final odometer reading, $r_2=3800km$
Time taken, $t=20hours$

As the initial position is the same as the final position,
Displacement of the car, $s=0km$

Odometer reads the total distance covered by the car till the given point of time. Hence, the distance covered by the car is the difference of the odometer readings. Hence, the distance covered is:
$d=r_2-r_1$
$d=3800-2200=1600km$

Now, using the definitions for velocity and speed,
$\text{Average velocity}=\frac{\text{Displacement}}{\text{Time}}$
$\text{Average velocity}=0$

$\text{Average speed}=\frac{\text{Distance}}{\text{Time}}$
$\text{Average speed}=\frac{1600km}{20h}$
$\text{Average speed}=80\text{kmph}$

Therefore, the average velocity of the car is 0 kmph, and the average speed of the car is 80 kmph.