Question

Explain the meaning of position, displacement, and distance traveled as they apply to an object moving along a line.

Short answer

Answer: Position refers to the location of an object relative to a reference point, while displacement represents the change in position, taking both magnitude and direction into account. On the other hand, distance traveled is the total length of the path taken by the object, considering only the magnitude of the motion, not its direction.

Step-by-step solution

Defining "Position"

The position of an object is a point in space that represents its location relative to a reference point, usually denoted as the origin. In one-dimensional motion, the position is expressed as a scalar quantity, either positive or negative. Positive values indicate the object is to the right of the origin, while negative values indicate it is to the left of the origin.

Defining "Displacement"

Displacement is a vector quantity that represents the change in an object's position. It is calculated as the difference between the final and initial positions of the object. Displacement takes both magnitude and direction into account. The magnitude of the displacement is the shortest distance between the initial and final positions, and the direction is the orientation of that distance. Displacement can be either positive or negative, depending on the direction of motion.

Defining "Distance Traveled"

Distance traveled is the total length of the path taken by the object during its motion. Unlike displacement, distance traveled is a scalar quantity, and it only takes into account the magnitude of the motion, not its direction. Distance traveled will always be equal to or greater than the magnitude of the displacement.

Example: Understanding Position, Displacement, and Distance Traveled

Let's imagine an object moving along a line, starting at the origin (0 meters). The object moves 3 meters to the right, stops, and then moves 2 meters to the left. Position: 1. Initial position: 0 meters 2. Position after moving to the right: +3 meters 3. Position after moving to the left: +1 meter (3 meters - 2 meters) Displacement: 1. The displacement is the difference between the final and initial position: +1 meter (final position) - 0 meters (initial position) = +1 meter. The positive value indicates motion to the right. Distance Traveled: 1. The object traveled 3 meters to the right and then 2 meters to the left, accumulating a total distance traveled of 5 meters. In summary, position describes the location of an object in relation to a reference point, displacement is the change in position (accounting for direction), and distance traveled is the total length covered by an object during its motion.