Explanation:

When a particle moves along a circular path of radius R, it completes one revolution after it has traveled a distance equal to the circumference of the circle. The circumference of a circle is given by the formula:

C = 2πR

So, in one complete revolution, the particle travels a distance of 2πR.

Distance:

The distance traveled by the particle after one complete revolution is 2πR.

Displacement:

The displacement of the particle after one complete revolution depends on the starting point and the ending point of the particle. If the particle starts and ends at the same point, then the displacement is zero. However, if the particle starts and ends at different points, then the displacement is given by the difference between the final and initial positions of the particle.

Assuming that the particle starts at point A and ends at point B, the displacement of the particle after one complete revolution is given by the vector AB, where A and B are two points on the circle.

The magnitude of the displacement vector AB is given by the length of the arc AB on the circle. The length of the arc AB is given by the formula:

s = Rθ

where θ is the angle subtended by the arc AB at the center of the circle. Since the particle has completed one revolution, the angle θ is equal to 2π radians.

Therefore, the magnitude of the displacement vector AB is given by:

s = R(2π) = 2πR

The direction of the displacement vector AB is along the tangent to the circle at point A.

Conclusion:

In conclusion, the distance traveled by the particle after one complete revolution is 2πR, and the displacement of the particle depends on the starting and ending points on the circle. If the particle starts and ends at the same point, then the displacement is zero. However, if the particle starts and ends at different points, then the displacement is 2πR along the tangent to the circle at the starting point.