Final answer:
The length of an arc can be calculated using the formula S = rθ, where S is the arc length, r is the radius, and θ is the angle in radians. Without additional specific information, such as the angle subtended by the arc or the fraction of the circle the arc represents, the calculation cannot be carried out.
Step-by-step explanation:
The question asks us to find the length of an arc on a curve between two points P and Q. The length of an arc on a circle can be computed if the radius and the angle in radians that the arc subtends at the center of the circle are known. The formula to calculate the arc length is S = rθ, where S is the arc length, r is the radius, and θ is the angle in radians.
From the context provided, it seems we are dealing with circular motion or geometry without a specific radius or angle provided. Typically, if we knew the angle a of the circle that the arc covers, we could use the fraction of the total circumference the angle represents to find the arc length. For example, if the angle a was 120 degrees in a full circle (360 degrees), the arc length would be one-third of the total circumference of the circle, which is 2πr.
Since the question does not provide the angle or the radius, we are unable to directly calculate the arc length. Additionally, the options provided (2/3π, 3/4π, 5/6π, 4/5π) do not have enough context to be matched to a specific calculation without additional information. Therefore, to accurately answer this question, we would need the specific angle subtended by the arc at the center of the circle or the fraction of the circle that the arc represents.