A particle is moving along a circular path of radius 5m with uniform speed 5/2 m/s. What will be average acceleration over a quarter circle?

Question

Answer

Given information:

Radius of the circular path (r) = 5 m

Uniform speed of the particle (v) = 5/2 m/s

Calculating the time taken to cover a quarter circle:

Length of a quarter circle = (1/4) * circumference of the circle

Circumference of the circle = 2 * π * r

Length of a quarter circle = (1/4) * 2 * π * r = (1/2) * π * r

Time taken to cover a quarter circle = distance / speed = [(1/2) * π * r] / (5/2) = (π * r) / 5

Calculating the change in velocity:

Change in velocity = final velocity - initial velocity

As the speed is constant, the change in velocity is zero.

Calculating the average acceleration:

Average acceleration = change in velocity / time

Since the change in velocity is zero, the average acceleration is also zero.

Explanation:

The average acceleration of the particle over a quarter circle is zero. This is because the particle is moving with a uniform speed, which means its velocity is constant. As the particle moves along the circular path, its direction changes continuously, but the magnitude of its velocity remains the same. Therefore, there is no change in velocity and hence no acceleration.

The time taken to cover a quarter circle can be calculated using the distance formula. Since the particle is moving with a uniform speed, the distance covered is equal to the length of a quarter circle. By dividing the distance by the speed, we can find the time taken to cover the quarter circle. In this case, the time taken is (π * r) / 5.

It is important to note that although the particle is constantly changing its direction, its speed remains the same throughout the motion. This is known as uniform circular motion. In this case, the average acceleration is zero, indicating that there is no change in velocity or speed over the quarter circle.

In conclusion, the average acceleration of the particle over a quarter circle is zero, and the time taken to cover the quarter circle is (π * r) / 5.

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