Explain (wit diagram) how uniform circular motion is an example of an accelerated motion?

Acceleration describes the change in velocity which is the vector, therefore, velocity may chage its magnitude and direction. Each case is described by the component of acceleration.

The change in magnitude of velocity is described by tangential component of acceleration
a(tangential) = dv/dt.
The change in direction of velocity is described by normal component of acceleration ((or centripetal acceletarion)
a(normal) = v²/R.
Unoform circular motion : constant magnitude, changing direction => centripetal acceleration

Uniform circular motion is considered an example of accelerated motion because even though the speed of the object remains constant, its direction constantly changes. This means that there is a change in velocity, which is a vector quantity.

To explain this visually, we can use a diagram:

1. Start by drawing a circle in the middle of a blank piece of paper. Label it as "Object's Path."

2. Next, draw an arrow on the circle to represent the object. Label it as "Object."

3. To indicate the acceleration, draw an arrow pointing towards the center of the circle from the object's initial position. Label it as "Acceleration."

4. Now, draw velocity vectors at different positions on the circle, always perpendicular to the tangent of the circle at that point. Label these vectors as "Velocity."

5. Connect the velocity vectors with arrows to show that they are all of the same length, representing a constant speed.

6. Finally, draw acceleration vectors at different positions on the circle. These vectors should always be pointing towards the center of the circle and perpendicular to the velocity vectors.

The diagram should demonstrate that the object is constantly changing its velocity at every point around the circle due to the centripetal acceleration, even though its speed remains constant. This change in velocity signifies an accelerated motion.

Remember, the key concept here is that acceleration is a change in velocity, which is a vector. In uniform circular motion, even though the object's speed is constant, the direction of the velocity is continuously changing, resulting in an acceleration towards the center of the circle.

Uniform circular motion refers to the motion of an object moving in a circular path with a constant speed. Although the speed remains constant, this type of motion is considered to be an example of accelerated motion because the direction of the velocity keeps changing. I will explain this concept using a diagram.

Consider an object moving along a circular path, as shown below:

```
^ v
|
|
<------O------->
|
|
|
|
```

In the diagram, the object is moving in a clockwise direction along the circular path. The velocity vector, represented by "v," indicates the direction of the object's motion at a given instant. At point A, the object is moving horizontally to the right. As the object moves from A to point B, its velocity vector gradually rotates towards the downward direction. At point C, the velocity vector is completely downward. Finally, as the object moves from point C back to point A, the velocity vector continues to rotate until it becomes horizontal again.

This change in the direction of velocity indicates that the object is experiencing acceleration. Acceleration is defined as any change in velocity, which includes not only changes in speed but also changes in direction. In uniform circular motion, the object's speed remains constant, but its velocity is constantly changing due to the changing direction.

In conclusion, the uniform circular motion is an example of accelerated motion because although the speed remains constant, the object experiences a continuous change in velocity due to its changing direction.