Question

A student analyzed the motion of an abject in two different ways. In one, she summed up the distances traveled by the object. In the other, she added the displacement vectors. The distance was sum was a large, positive number, while the sum of the vectors was one short displacement vector with a small positive magnitude. Which of the following statements is most likely true?

A. The student made a mathematical error in the distance summing
B. The student should have added the distances to the displacements
C. The object's final location was near its initial location
D. The magnitude of the sum of the displacement vectors should have been the same as the sum of the differences.

Answer 1

The student made a mathematical error in the distance summing. Distance traveled is a scalar quantity that represents the total path length, while displacement is a vector quantity that represents the change in position with direction.

Step-by-step explanation:

The student made a mathematical error in the distance summing. When summing the distances traveled by the object, the student likely added all the magnitudes of the individual displacements without considering their directions. This resulted in a large, positive number as the distance sum. In contrast, when adding the displacement vectors, the direction of each displacement is taken into account, resulting in a single displacement vector with a small positive magnitude.

It is important to understand that distance traveled is a scalar quantity that represents the total length of the path taken, irrespective of the direction. On the other hand, displacement is a vector quantity that represents the change in position from the initial to the final location, taking into account both magnitude and direction.