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Home Concept Builders 1D Kinematics Distance vs. Displacement Help Help 1

Distance vs. Displacement - Questions 1 Help

Distance is a scalar quantity that refers to the amount of ground that is covered by a moving object. Distance is ignorant of direction. The value of distance will be the same whether or not there is a change in direction. Displacement is a vector quantity that refers to the overall change in position of an object. Displacement is measured from the starting position to the final position. The direction of this displacement is simply the direction one must move to reach the final position when starting at the initial position.

There are four versions of this question. Here is one of the versions:

A dog walks 12 meters to the east and then 16 meters back to the west.
For this motion, what is the distance moved?
What is the magnitude and direction of the displacement?

Other versions of this question simply use different numbers and directions.

This question is an Apprentice-level, two-segment motion. There is the eastward movement followed by the westward movement. When it comes to the direction-ignorant distance quantity, these directions do not matter. Simply add up the length of the two distance segments and you have calculated the amount of ground that is covered.

The quantity displacement is a direction-conscious quantity. Direction matters! The eastward movement of motion takes the dog away from the starting position. But the westward movement negates this motion and takes the dog back past the starting point to the westward side of the starting position. Because the second movement is in the opposite direction as the first segment, one must subtract this from the length of the first movement.

A common approach for questions like these involves defining East as the positive direction and West as the negative direction. A 16-meter westward segment is thought of as a -16 m displacement. The overall displacement is the sum of the positive (East) and negative (West) movements. If the sum turns out to be negative, then the direction is opposite of East; that is, it would be West.

Finally, as questions like these become more difficult (as in the 3-segment "Master" level and 4-segment "Wizard" level questions), it becomes useful to diagram the situation. Draw an arrow for each segment of the motion; and draw the arrow in the described direction and approximately the relative length. Where one arrow ends, the next arrow begins. The process of diagramming helps a learner to visualize displacement as the overall change in position relative to the starting position.

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