Question

A car is moving along a straight line OP as shown in the figure. It moves from O to P in 18 s and returns from P to Q in 6 s. Which of the following statements is not correct regarding the motion of the car?

• A. The average speed of the car in going from O to P and come back to Q is 20 m $s^{-1}$.
• B. The average velocity of the car in going from O to P and come back to Q is 10 m $s^{-1}$.
• C. The average speed of the car in going from O to P and come back to O is 20 m $s^{-1}$.
• D. The average velocity of the car in going from O to P and come back to O is 20 m $s^{-1}$.

Answer 1

The correct option is D The average velocity of the car in going from O to P and come back to O is 20 m $s^{-1}$.

(a) As the car goes from O to P:

Since the car moves in a straight line, the distance will be equal to the displacement.

Total distance $=$ Total displacement$=360$

The time taken by the car is$=18sec$

Average speed of car is given by:

$v_{avg}=\frac{\text{Total distance}}{\text{Total time taken}}$

$=\frac{360}{18}=20m/s$

Average velocity of the car is given by:

$=\frac{\text{Total displacement}}{\text{Total time taken}}$

$=\frac{360}{18}=20m/s$

(b)As the car goes from O to P and then back to O:

Total distance covered by car $=360+(360-240)=360+120=480m$

The total displacement of car $=240m$

Total time taken $=18+6=24sec$

Average speed

$=\frac{480}{24}=20m/s$

Average velocity

$=\frac{240}{24}=10m/s$

Hence, option $\left(D\right)$ is correct.