Question

Displacement: Consider a deer that runs from point A to point B. The distance the deer runs can be greater than the magnitude of its displacement, but the magnitude of the displacement can never be greater than the distance it runs. True or False?

Answer 1

The given statement concerning distance and displacement is true.

Step-by-step explanation:

If any point travels along any path between two points A and B the distance it travels is the length of the actual path it travels.

Mathematically the distance between two points is the algebraic sum of the infinitesimal distances that the particle travels.

Mathematically
`S=\int |ds|`

Displacement by definition is the shortest distance between the initial and final positions of the particle and is given by the straight line joining the two points.

Since a line is the shortest path that exists between 2 points thus it will be always smaller than any other path connecting the 2 points hence will be smaller than the distance.

While as if the object travels along a straight line without changing it's direction the distance in that case equals the displacement.