By definition, the annual parallax of a star π is the angle at which a segment r is seen from this star, equal to the average distance of the Earth from the Sun (1 AU). If we express the distance from the Sun to the star L in parsecs, and the parallax in arc seconds, then π ″ = 1 AU. / L (pc). The proper motion µ is the angular velocity of the star across the sky. If during time T the star has passed the distance D perpendicular to the line of sight, then µ ″ = D (AU) / L (pc) T. By the condition of the problem, the displacement of the star in time T, equal to 1 year µ ″ T = π ″, hence it turns out that during this time the star has passed the distance D equal to 1 AU. This can also be directly verified from the definition of these quantities. The tangential speed of the star in relation to the Sun is vT = D / T = 1 AU. / 1 year = 1.5⋅108 km / 3.156⋅107 s = 4.74 km / s.
Remember: The process of learning a person lasts a lifetime. The value of the same knowledge for different people may be different, it is determined by their individual characteristics and needs. Therefore, knowledge is always needed at any age and position.