Question

question 3 (1 point) saved
suppose that an object travels from one point in space to another. make a comparison between the magnitude of the displacement and the distance traveled by this object.

a) the displacement can be either greater than, smaller than, or equal to the distance traveled.

b) the displacement is either greater than or equal to the distance traveled.

c) the displacement is always equal to the distance traveled.

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

Explanation:

To determine the correct option, we analyze the concepts of displacement and distance traveled:

• Distance traveled is the total length of the path an object takes.
• Displacement is the straight - line distance between the initial and final positions of the object, along with its direction.

When an object moves in a straight line without changing direction, the magnitude of displacement (the length of the straight - line path) is equal to the distance traveled (the length of the actual path, which is also a straight line in this case).

When an object moves along a non - straight path (for example, it curves or changes direction multiple times), the distance traveled (the sum of the lengths of all the segments of the path) will be greater than the magnitude of the displacement (the straight - line distance between the start and end points).

So, the magnitude of displacement can never be greater than the distance traveled. It can only be less than (when the path is non - straight) or equal to (when the path is straight) the distance traveled.

Let's analyze each option:

• Option a: Displacement cannot be greater than distance traveled, so this is incorrect.
• Option b: Displacement is not greater than distance traveled, so this is incorrect.
• Option c: Displacement is only equal to distance traveled when the motion is in a straight line without any change in direction. In most cases of non - straight - line motion, displacement is less than distance traveled, so this is incorrect.
• Option d: This option correctly states that the displacement is either less than or equal to the distance traveled.

Answer:

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