Final answer:
With radial acceleration at zero and nonzero tangential acceleration, the object is in linear motion with its velocity changing; it is not in circular motion, and it is neither at rest nor moving at constant speed.
Step-by-step explanation:
If arad = 0 (radial acceleration is zero) and atan ≠ 0 (tangential acceleration is not zero), we can conclude about the object's motion that it is moving in linear, rather than circular or rotational, motion. This is because radial acceleration occurs when an object moves along a curved path, and in the case of circular motion, radial acceleration points towards the center of the circle, causing the object to change direction while maintaining constant speed. Since arad is zero, there's no change in direction, indicating no centripetal force and thus no circular motion.
Conversely, having a nonzero tangential acceleration atan indicates that the object's speed is changing over time. Thus, we conclude the object is not at rest but moving with a changing velocity - either speeding up or slowing down along a straight path. If a constant, nonzero force is applied, the velocity and acceleration of an object would change consistently in the direction of the applied force.
Summarizing, an object with no radial acceleration but nonzero tangential acceleration is in linear motion with a changing velocity. This can happen when the object is either speeding up or slowing down in either the positive or negative direction, but not moving in a circular path.