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

When a particle moves in a circular path with a uniform (constant) speed, the magnitude of its velocity vector stays the same, but the direction of the velocity continuously changes as the particle goes around the circle.

Velocity is a vector quantity defined as $v=v·u$, where v is the speed (a scalar) and u is a unit vector pointing in the direction of motion. Since the direction of u changes at every instant of a circular motion, the velocity vector $v$ is not constant; it varies in direction while its magnitude remains constant.

Acceleration is the time derivative of velocity: $a=\; dv/dt$. Because the direction of the velocity vector changes, its derivative is non‑zero, giving a non‑zero acceleration even though the speed does not change. This acceleration always points toward the centre of the circular path and is called **centripetal acceleration**.

The magnitude of the centripetal acceleration is given by

$a=\frac{v}{r^2}$

where $v$ is the constant speed and $r$ is the radius of the circle. Since the particle continues to move around the circle, the direction of this acceleration vector also constantly changes, always pointing toward the instantaneous centre of the circle.

Thus, both the velocity vector (changing direction) and the acceleration vector (changing direction) vary with time, even though the speed and the magnitude of the acceleration remain constant. Therefore, the correct statement is that the particle has **varying velocity and varying acceleration**.