A car is travelling along circular track at constant speed 20m/s has completed half revolution on the track .Its average velocity will be
a.10pi m/s
b.20/pi m/s
c.20 m/s
d.40pi m/s

To determine the average velocity of a car traveling along a circular track at a constant speed of 20 m/s after completing half a revolution, we need to understand the concepts of displacement and time. Average velocity is defined as the total displacement divided by the total time taken.

Understanding Displacement in Circular Motion

When the car completes half a revolution on a circular track, it moves from one point on the circumference to the point directly opposite. This means that while the car has traveled a distance along the circular path, its displacement—the straight-line distance from the starting point to the ending point—is actually the diameter of the circle.

Calculating Displacement

Let’s denote the radius of the circular track as r. The diameter, which represents the displacement after half a revolution, is given by:

• Diameter = 2r

Calculating Time Taken

Next, we need to calculate the time taken to complete half a revolution. The circumference of the entire circular track is:

• Circumference = 2πr

Since the car completes half a revolution, the distance traveled is:

• Distance = πr

Now, using the speed of the car (20 m/s), we can find the time taken to travel this distance:

• Time = Distance / Speed = (πr) / (20 m/s)

Calculating Average Velocity

Now that we have both displacement and time, we can calculate the average velocity:

• Average Velocity = Displacement / Time

Substituting the values we have:

• Average Velocity = (2r) / [(πr) / (20)]

When we simplify this expression, we can cancel out r:

• Average Velocity = (2r * 20) / (πr) = 40 / π

Final Answer

Thus, the average velocity of the car after completing half a revolution is:

• Average Velocity = 40/π m/s

From the options provided, the correct answer is d. 40/π m/s.