**Uniform Circular Motion**

Uniform circular motion refers to the motion of an object traveling in a circular path at a constant speed. In this type of motion, the object moves along the circumference of the circle, maintaining a fixed distance from the center.

**Acceleration in Uniform Circular Motion**

While the speed of the object remains constant in uniform circular motion, it is important to note that the object is still experiencing acceleration. This may seem counterintuitive since we typically associate acceleration with a change in speed. However, in uniform circular motion, the acceleration is directed towards the center of the circle and is known as centripetal acceleration.

**Direction of Motion Changes**

The correct answer to why uniform circular motion is called continuously accelerated motion is that the direction of motion changes. In uniform circular motion, an object continuously changes its direction as it moves along the circular path. This change in direction implies that the object is experiencing acceleration.

**Velocity Remains the Same**

While the object is undergoing acceleration in uniform circular motion, its velocity remains constant. Velocity is a vector quantity that includes both magnitude (speed) and direction. In uniform circular motion, the speed of the object remains constant, but its direction changes. Therefore, the velocity of the object remains the same in terms of magnitude, but the direction of the velocity vector continually changes.

**Centripetal Acceleration**

The centripetal acceleration is the acceleration experienced by an object undergoing uniform circular motion. It is directed towards the center of the circle and is responsible for continuously changing the direction of the object's motion. The magnitude of the centripetal acceleration can be calculated using the formula:

a = v^2 / r

where a is the centripetal acceleration, v is the velocity of the object, and r is the radius of the circular path.

**Conclusion**

In conclusion, uniform circular motion is called continuously accelerated motion because the direction of motion of the object undergoing circular motion continually changes. Although the speed (magnitude of velocity) remains constant, the object experiences centripetal acceleration directed towards the center of the circle. This acceleration is responsible for continuously changing the direction of the object's motion, making it an example of accelerated motion.