Final answer:
In uniform circular motion, the instantaneous velocity is always tangent to the path and the tangential velocity vector is always perpendicular to the radius of the circular path. Therefore, the correct answer is option A, perpendicular to the path.
Step-by-step explanation:
In curvilinear motion, specifically in uniform circular motion, the direction of the instantaneous velocity is always tangent to the path that the object is following. This means that the correct answer to the question is A. Tangent to the path.
Conversely, since velocity is tangential, the acceleration in circular motion is directed towards the center of the circle, which means it is always perpendicular to the velocity. This centripetal acceleration is a result of the centripetal force, which is required to keep the object moving in a circular path.
Additionally, the tangential velocity vector in uniform circular motion is always perpendicular to the radius of the circle. Therefore, we can deduce that linear velocity is tangent to the circular path, confirming that the instantaneous velocity is indeed tangent to the path.
In curvilinear motion, the direction of the instantaneous velocity is always A. Tangent to the path. This means that the velocity vector points in the direction of the tangent line to the curve at a given point.
For instance, in uniform circular motion where an object moves in a circular path at constant speed, the instantaneous velocity is always tangential to the path on the circle.
Therefore, the correct answer is option A, perpendicular to the path.