The second question:

The third question:

The fourth question:

The fifth question:

The sixth question:

This part of the extended materials mainly examines the knowledge points of the unit vector:

If the particle moves along the plane curve C, the acceleration vector A can be decomposed into two components along the tangent direction and normal direction of the trajectory. Let a point on the curve C be the origin O of the arc length coordinate S. When moving in one direction along the trajectory tangent, the trajectory arc length S increases, and when moving in the other direction along the trajectory tangent, the trajectory arc length S decreases.

I is the unit vector along the tangent direction of the trajectory and pointing to the increasing direction of the arc length s of the trajectory, J is the unit vector along the normal direction of the trajectory and pointing to the concave side of the curve, and θ is the included angle between the tangent direction of the trajectory and the X axis, as shown in figure 1. I, j and dθ satisfy the following relationship.

Sinusoidal curves have both convex and concave parts and inflection points. The definitions of arc length coordinate S, unit vector I and j are the same as above, and θ is still the included angle between the advancing direction of orbital unit vector I and X axis.