A particle moving with uniform speed in a circular path maintains:

The correct option is: Varying velocity and varying acceleration.

Let us analyze the motion of a particle moving with a uniform speed (constant magnitude of velocity) in a circular path step-by-step:

1. Understanding Velocity:
Velocity is a vector quantity, which means it has both magnitude (speed) and direction. Even though the particle moves with a uniform speed, its direction of motion changes continuously at every point along the circular path. Since the direction changes, the velocity vector is not constant. Therefore, the particle has a varying velocity.

2. Understanding Acceleration:
Acceleration is also a vector quantity defined as the rate of change of velocity. For a particle in uniform circular motion, there is an acceleration directed towards the center of the circle, known as centripetal acceleration.
The magnitude of this acceleration is given by:
$a=\frac{v^2}{r}$
where $v$ is the constant speed and $r$ is the radius of the circular path. While the magnitude of this acceleration remains constant, its direction is always pointing towards the center of the circle. As the particle moves along the circle, the direction of this acceleration vector continuously changes. Because its direction changes, the acceleration vector is not constant. Therefore, the particle has a varying acceleration.

Conclusion:
A particle moving with uniform speed in a circular path maintains a varying velocity and a varying acceleration due to the continuous change in the direction of both vectors.