Final answer:
Tangential acceleration refers to acceleration tangent to the path of motion. In circular motion, this is directly related to angular acceleration. The given function r(t) = ln(t)i represents linear motion and does not immediately provide information related to circular motion or tangential acceleration without additional context.
Step-by-step explanation:
The given function r(t) = ln(t)i implies a motion along a path where the position vector is expressed in terms of the natural logarithm of time. When dealing with tangential acceleration, we are referring to the acceleration that is tangent to the path of the motion of an object. In circular motion, this concept becomes more distinct as the tangential acceleration is specifically the acceleration in the direction tangent to the circle at the point of interest.
Tangential acceleration is given by at = rα, where r is the radius and α is the angular acceleration. In rotational motion, linear or tangential acceleration, denoted by a, can also be expressed as a = rωα, with ω representing angular velocity. It's important to note that for any rotational motion, it's assumed that the angular acceleration is constant.
If we were to apply this to the given function, we would need to differentiate it with respect to time to find the corresponding velocity and then differentiate again to find the tangential acceleration. However, it should be noted that without a clear indication of circular motion or a radius, the function provided does not directly give us radial or tangential components.