The ratio of displacement to distance is always:

Correct option is D

The correct answer is (d) Is equal to or less than one.

The ratio of displacement to distance measures how the shortest path (displacement) compares to the total path traveled (distance). This ratio can never exceed 1 because:

• Displacement is the shortest straight-line distance between the initial and final points of a journey.
• Distance is the total path traveled, which is always greater than or equal to the displacement.

Key Cases:

• When the ratio equals 1:

  • This occurs when the object moves in a straight line in a single direction without changing its path.
  • Example: A car traveling 10 km in a straight line from point A to point B. Here, displacement = distance = 10 km.

• When the ratio is less than 1:

  • This occurs when the object takes a curved or zigzag path. The distance traveled is greater than the straight-line displacement.
  • Example: A car traveling along a circular path from one point to another. The displacement is the straight-line distance between the points, but the distance is the length of the curved path.

Formula:

Ratio of displacement to distance=DisplacementDistance\text{Ratio of displacement to distance} = \frac{\text{Displacement}}{\text{Distance}}Ratio of displacement to distance=

Additional Information:

• Is less than one: True for most cases but not always; the ratio can also be equal to one.
• Is equal to one: True only when the displacement equals the distance (straight-line motion).
• Is more than one: Incorrect because displacement can never exceed distance.