Chapter 2.2, Problem 10SSC

To determine

Whether two friends using coordinate system with different origin point (one using grocery store while another using post office) agree on the car’s position, displacement, distance, time interval taken by the trip.

Answer to Problem 10SSC

The two friends agree on the car’s displacement, distance, time interval taken by the trip.

The two friends disagree on the position of the car.

Explanation of Solution

Introduction: In the study of motion of any object, the coordinate system provides information regarding the origin point of the variable (say distance covered by object) and the direction in which the value of the variable increases. The origin point in a coordinate system refers to the point where the value of the variable is zero.

Consider a car moves from grocery store to the post office.

Two friend uses coordinate system to represent the motion.

The first person uses the coordinate system with the origin at the post office and the direction of motion of car as positive direction.

The second person uses the coordinate system with the origin at the post office and the direction opposite to the direction of motion of car as positive direction.

Irrespective of the origin of the coordinate system, the total displacement, total distance covered, and the total time taken for the trip will be the same for both the friends as these variables is independent of the origin of the coordinate system. Hence, the two friends agree on the car’s displacement, distance, time interval taken by the trip.

The position of the car in a coordinate system is taken from origin of the coordinate system. At a particular time, the car’s position will be different for both the persons as the origin of the coordinate system taken by both the persons is different from each other.

Conclusion:

Thus, the two friends agree on the car’s displacement, distance, time interval taken by the trip whereas, the friends disagrees on the position of the car.