an object is undergoing uniform circular motion. which of the following statements is true?

a. the velocity is constant
b. the acceleration is constant.
c. the a is constant but v varies.
d. the v is constant but the a varies.
E. both a and v vary.

To determine which statement is true regarding an object undergoing uniform circular motion, we need to understand the characteristics of such motion.

In uniform circular motion, the object moves along a circular path at a constant speed but constantly changes its direction. This means that the object continuously accelerates towards the center of the circle, providing a centripetal acceleration.

Now, let's analyze each statement:

a. The velocity is constant.
This statement is not true in the case of uniform circular motion. Although the speed remains constant, the direction of the object's motion changes continuously, indicating that the velocity is not constant.

b. The acceleration is constant.
This statement is also not true. While the object experiences acceleration, it is not constant. The acceleration is always directed towards the center of the circle, known as centripetal acceleration. However, the magnitude of this acceleration remains constant unless an external force is acting on the object.

c. The acceleration is constant, but velocity varies.
This statement is incorrect. As explained earlier, the acceleration in uniform circular motion is always directed towards the center of the circle, but the magnitude of the acceleration remains constant.

d. The velocity is constant, but acceleration varies.
This statement is incorrect, as the velocity is not constant during uniform circular motion due to the changing direction.

e. Both acceleration and velocity vary.
This statement is correct. In uniform circular motion, both acceleration and velocity vary. The velocity changes continuously due to the change in direction, while the acceleration remains constant in magnitude but changes its direction towards the center of the circle.

Therefore, the correct answer is (E) – both acceleration and velocity vary.

The correct answer is d. The velocity (v) is constant, but the acceleration (a) varies.

In uniform circular motion, the object moves in a circular path at a constant speed. The velocity is the rate at which the object changes its position, and in uniform circular motion, the object's velocity remains constant in terms of magnitude (speed). However, the object is constantly changing direction, which means its velocity is changing in terms of direction. This change in direction indicates that the object is experiencing acceleration.

The acceleration in uniform circular motion is directed towards the center of the circle and is called centripetal acceleration. Its magnitude is given by the equation a = v^2/r, where v is the magnitude of the velocity and r is the radius of the circle. As the object moves along the circle, the acceleration changes because the velocity and radius remain constant.

v is changing direction, and a is also changing direction.

so, what do you think?