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Home Concept Builders 1D Kinematics Distance vs. Displacement Help Help 8

Distance vs. Displacement - Questions 8 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 football coach walks 12 meters westward, then 16 meters eastward, then 22 meters westward, and finally 6 meters eastward.
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 a Wizard-level, four-segment motion. There are two westward movements and two eastward movements. When it comes to the direction-ignorant distance quantity, these directions do not matter. Simply add up the length of the four movements and you have calculated the amount of ground that is covered.

The quantity displacement is a direction-conscious quantity. Direction matters! Both westward movements take the football coach away from the starting position; they add together to give the football coach a westward displacement. But the eastward movements negate these motions and take the football coach back towards the starting point (but not past it). To determine the overall displacment or change in position, these two eastward movements must be subtracted from the two westward movements.

A common approach for questions like these involves defining East as the positive direction and West as the negative direction. A 12-meter westward movement is thought of as a -12 m displacement. The overall displacement is the sum of two positive (East) and two 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, this 4-segment "Wizard" level question is more difficult. As such, it becomes useful to learn 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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Distance and Displacement

Representing Vector Addition with Diagrams

Concept Builder Teacher Notes Directions