Final answer:
The question involves calculating the linear distance traveled along a circular path using the formula x = rω. This is commonly used in physics to relate linear and angular displacements. Without additional context or the angular displacement (θ), it is not possible to solve for the linear distance in the student's question.
Step-by-step explanation:
The student's question appears to be related to the calculation of linear distances traveled along a circular path using the formula x = rω, where x represents the linear distance, r is the radius of the circular path, and ω (omega) is the angular displacement in radians. This formula is derived from the concept of arc length in a circle and is a crucial part of understanding circular motion in physics. For example, using the provided formula, if a train's wheels have a radius of 0.350 m and rotate through an angle of 1257 radians, the distance x the train moves down the track can be calculated by substituting the known values into the equation, resulting in x = (0.350 m)(1257 rad) = 440 m.
In the case of the student's question with the variables r = 5 miles, s = 3 miles, and θ (theta) unknown, they may be referring to the formula s = rθ. However, without additional context about the variable θ or what the question is asking to solve for, it is difficult to provide a specific answer. If the question is to find the distance along the arc (in this case, represented by variable 's'), then the problem needs the angular displacement (θ) to solve for the arc length or the linear distance using the formula s = rθ.