Question

question 17 (1 point)
suppose that an object travels from one point in space to another. make a comparison between the displacement and the distance traveled.
the displacement is either greater than or equal to the distance traveled.
the displacement is always equal to the distance traveled.
the displacement is either less than or equal to the distance traveled.
the displacement can be either greater than, smaller than, or equal to the distance traveled.

Explanation:

• Distance: It is a scalar quantity that represents the total path length an object travels. For example, if an object moves along a zig - zag path, the distance is the sum of the lengths of all the segments of the path.
• Displacement: It is a vector quantity. It is defined as the straight - line distance from the initial position to the final position of the object. Mathematically, if the initial position vector is \(\vec{r}_i\) and the final position vector is \(\vec{r}_f\), then displacement \(\vec{d}=\vec{r}_f-\vec{r}_i\), and its magnitude \(d = |\vec{r}_f-\vec{r}_i|\).
• Comparison:
• When an object moves in a straight line without changing direction, the displacement magnitude is equal to the distance traveled. For example, an object moving from point \(A\) to point \(B\) in a straight line, if \(A\) and \(B\) are separated by a distance \(s\), then distance \(D = s\) and displacement magnitude \(d=s\).
• When an object moves in a non - straight path (e.g., a circular path for a partial or full revolution), the distance traveled is greater than the displacement magnitude. For a full - circle motion of radius \(r\), the distance \(D = 2\pi r\), and the displacement (if it returns to the starting point) is \(d = 0\). In general, using the triangle inequality (in the context of vectors and path lengths), we know that \(d\leq D\)

Answer:

The displacement is either less than or equal to the distance traveled.