A

To analyze the motion of a point A on the rim of a rolling wheel, we consider the following:

**Step 1**: Define the motion of the wheel.
- The wheel rolls without slipping along the x-axis with a constant linear speed, say speed $v$.
- The center of the wheel moves along the x-axis, tracing a linear path.

**Step 2**: Determine the relationship between linear speed and angular speed.
- The angular speed $\omega$ of the wheel is related to its linear speed $v$ and radius $r$ as follows:
$$ \omega = \frac{v}{r} $$

**Step 3**: Analyze the path traced by point A.
- As the wheel rolls, point A moves in a circular path around the center of the wheel. The position of point A at time $t$ can be described with respect to the center of the wheel's position:
- The center of the wheel is located at position $(vt, r)$ (if at time $t=0$ it is at the origin).
- The coordinates of point A, which moves in a circular motion around this center, can be expressed as:
$$ (x_A, y_A) = (vt - r \sin(\theta), r - r \cos(\theta)) $$
where $\theta = \omega t = \frac{v}{r}t$. This captures the circular motion of A as the wheel rolls.

**Step 4**: Describe the overall motion.
- In this scenario, point A undergoes both rotation around the wheel's center and translation due to the motion of the center itself. The resulting path will be a cycloid - a curve traced by a point on the rim of a circle as it rolls along a straight line.

Therefore, the motion of point A starting from the origin as it rolls along the x-axis exhibits complex motion, representing both the circular motion about the center and the linear motion of the wheel.