Final answer:
A particle with constant angular velocity along a circle experiences radial acceleration keeping its speed constant and causing it to move along a circular path; the angular acceleration is zero. Option C is correct.
Step-by-step explanation:
When a particle is moving with constant angular velocity along a circle, it indeed experiences a radial or centripetal acceleration. This is true because, even though the speed of the particle remains constant, its direction is continuously changing. The radial acceleration is always directed towards the center of the circle and is necessary to keep the particle moving along the circular path.
The linear velocity of a particle in uniform circular motion can be described at any time t by taking the derivative of its position vector r(t).
For a particle with a constant angular frequency a = 4.00 rad/s, starting at position y = 0 m and x = 5 m at time t = 0, the position vector would be r(t) = (5 cos(at))i + (5 sin(at)). At t = 10 s, we substitute a and t to find the new position, as well as taking the derivative of r(t) to find the velocity and the second derivative to find the acceleration.
Since the angular velocity is constant, the angular acceleration is zero. The lack of tangential acceleration implies that we only deal with the centripetal or radial acceleration in this scenario. Furthermore, the particle is not moving in a straight line because it is constrained to move in a circular path by the centripetal force.