which one of the following statements is true about the motion of a particle in a circular path?
A. the centripetal acceleration is constant if the particle speed is constant.
B. the tangential acceleration can be perpendicular to the velocity vector of the particle
C. the centripetal acceleration is always in the direction perpendicular to the velocity of the particle
D. the acceleration is always perpendicular to the velocity of the particle

The centripetal acceleration of an object in a circular path is equal to the square of the speed divided by the radius of the path, and is always directed towards the center of the path. The object's velocity is tangential to the path.

A. This statement is true. Since ac = v²/r, the centripetal acceleration is constant if the velocity and radius are both constant.

B. This statement is false. The velocity vector is tangential, so it is parallel to the tangential acceleration, not perpendicular.

C. This statement is true. The centripetal acceleration is radial, and the velocity is tangential, so they are perpendicular to each other.

D. This statement is false. If there is no tangential acceleration, then the net acceleration is equal to the centripetal acceleration and will be perpendicular to the velocity. However, if there is tangential acceleration, then the net acceleration is not perpendicular to the velocity.