Here's how to determine the ratio of distance to displacement for a particle moving along a semicircle:

Understanding the Concepts

* Distance: The total path length traveled by the particle.

* Displacement: The straight-line distance between the starting and ending points.

Calculations

1. Distance: The distance covered along the semicircle is half the circumference of a full circle:

* Distance = (1/2) * 2πr = πr

2. Displacement: The displacement is the diameter of the circle:

* Displacement = 2r

3. Ratio: The ratio of distance to displacement is:

* Distance / Displacement = (πr) / (2r) = π/2

Therefore, the ratio of distance covered to displacement for a particle moving along a semicircle of radius 'r' is π/2.