Owl: Draw an arrow from the origin to a moving point. As time changes, the tip of that position vector r(t) traces a curve. The velocity vector r′(t) tells how the tip is moving — direction of the tangent and a magnitude that is speed.
Speed is a scalar; velocity is a vector. Mixing those is the headline misconception of this topic.
Position arrow tip traces a curve — what does the velocity arrow mean?
We'll differentiate component-wise, compare speed with velocity, and read tangent direction from r′.