Describe the path of a moving body whose acceleration is constant in magnitude at all times and is perpendicular to the velocity.

When the acceleration of a moving body is constant in magnitude and perpendicular to the velocity, the body follows a circular path. This scenario is known as uniform circular motion.

To describe the path, It's important to understand the key concepts involved:

1. Velocity: Velocity is the rate of change of displacement of an object with respect to time. In circular motion, velocity is not constant as it continuously changes direction. However, the speed remains constant.

2. Acceleration: Acceleration is the rate of change of velocity. In uniform circular motion, the acceleration always points towards the center of the circle and is perpendicular to the velocity.

3. Centripetal Force: The force required to keep an object moving in a circular path is called centripetal force. It acts towards the center of the circle and is provided by a tension force, friction, or gravity.

Now, let's discuss the path of the moving body:

1. Initially, the body has a certain velocity in a specific direction.

2. Due to the constant acceleration perpendicular to the velocity, the velocity continuously changes its direction while maintaining the same magnitude (speed).

3. As the body continues to move with a constant speed, it follows a circular path around a fixed center.

4. The centripetal force acting towards the center continually changes the body's direction but does not change its speed.

5. The body continues to move in a circular path until an external force, such as friction or a change in the applied force, acts on it.

In summary, a moving body with constant magnitude acceleration perpendicular to the velocity follows a circular path known as uniform circular motion. The body's speed remains constant while its direction changes continuously due to the centripetal force acting towards the center.

When the acceleration of a moving body is constant in magnitude and always perpendicular to the velocity, the body follows a particular path known as a circular path.

To understand this, let's break it down step by step:

1. Constant Acceleration: When the acceleration is constant, it means that there is a constant force acting on the body. This force is always directed towards the center of the circular path. For example, if you swing a ball on a string, the force you apply is constantly directed toward the center.

2. Perpendicular Acceleration: The acceleration being perpendicular to the velocity means that it acts at a right angle to the direction of motion. In other words, it is always directed towards the center of the circle, regardless of the body's position or speed along the path.

3. Circular Path: As a result of a constant magnitude and perpendicular acceleration, the body moves in a circular path. The velocity vector continuously changes its direction but maintains a constant speed. Thus, the body undergoes uniform circular motion.

To visualize this, imagine a car moving on a circular track. The car's velocity is always tangent to the track, while the acceleration points inward, toward the center of the circle.

In summary, when a body experiences constant acceleration perpendicular to its velocity, it follows a circular path. This scenario is known as uniform circular motion.

It is a circular path, but the direction of the accleration keeps changing. Acceleration is centripetal.