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Which statement best describes the difference between path length and displacement for an object moving in a straight line and returning to its starting point?
Path length is always equal to displacement
Displacement is greater than path length
Path length is either equal to or greater than displacement
Displacement is always negative Question ID : 4410092046104 Option 1 ID : 4410098056489 Option 2 ID : 4410098056491 Option 3 ID : 4410098056490 Option 4 ID : 4410098056492 Status : Answered Chosen Option : C
Path length is either equal to or greater than displacement
Remember that path length is the total distance covered (scalar), while displacement is the shortest straight-line vector distance between start and end points; scalar magnitude is always greater than or equal to vector magnitude.
Remember that path length is the total distance covered (scalar), while displacement is the shortest straight-line vector distance between start and end points; scalar magnitude is always greater than or equal to vector magnitude.
Define Path Length
Path length is the total distance traveled by an object along its actual trajectory. It is always positive and depends on the specific route taken.
Define Displacement
Displacement is the change in position of an object, defined as the shortest straight-line distance from the initial point to the final point, including direction.
Compare Values
When moving in a straight line and returning, the total path length is (distance to point + distance back). The displacement is (final position - initial position), which is 0. Since the object moved, path length > 0, so path length > displacement. If the object does not change direction, path length = displacement.
A: Path length is only equal to displacement if the motion is unidirectional, not when returning to the start; B: Displacement can never exceed path length due to the triangle inequality; D: Displacement is a vector and can be negative, zero, or positive, but it is not inherently 'always negative'.
C is correct because path length represents the total distance accumulated along the motion path, which will always be greater than or equal to the straight-line displacement between the start and end points.
In motion problems, always check if the path is linear and unidirectional; if the object reverses direction, displacement will always be strictly less than the path length.
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