We know that, average velocity=Total displacement/Total time

The average velocity of a car moving along a circular path can be determined by considering the displacement and the time taken. In this case, we need to find the average velocity when the car completes 1/4th of a revolution.

Displacement:

When the car completes 1/4th of a revolution, it covers an arc length equal to 1/4th of the circumference of the circle. The circumference of a circle is given by 2πR, where R is the radius of the circle. Therefore, the arc length covered by the car is (1/4) * 2πR = (π/2)R.

Time:

To find the time taken, we need to consider the period of the car's motion. The period is the time taken to complete one full revolution. Since the car is moving at a constant speed, the period can be calculated using the formula T = (2πR)/v, where v is the constant speed of the car.

The time taken to complete 1/4th of a revolution can be calculated by dividing the period by 4. Therefore, the time taken is T/4 = ((2πR)/v)/4 = (πR)/(2v).

Average Velocity:

The average velocity of the car can be calculated by dividing the displacement by the time taken. Therefore, the average velocity is ((π/2)R) / ((πR)/(2v)) = v.

Explanation:

The average velocity of the car when it completes 1/4th of a revolution is equal to its constant speed, v. This is because the car moves along the circular path with a constant speed, meaning its speed does not change. As a result, the average velocity over any interval of time is equal to the constant speed.

By considering the displacement and time taken, we can determine that the average velocity of the car is equal to its constant speed, v, when it completes 1/4th of a revolution.

Therefore, the average velocity of the car when it completes 1/4th of a revolution is v.