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Hold down the T key for 3 seconds to activate the audio accessibility mode, at which point you can click the K key to pause and resume audio. Useful for the Check Your Understanding and See Answers.

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 quarterback back pedals 2.2 meters southward and then runs 6.8 meters northward.
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 northward movement followed by the southward 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 southward segment of motion takes the quarterback away from the starting position. But the northward segment negates this motion and takes the quarterback back past the starting point to the northward side of the starting position. Because the second segment is in the opposite direction as the first segment, one must subtract this from the length of the first segment.

A common approach for questions like these involves defining North as the positive direction and South as the negative direction. A 2.2-meter southward movement is thought of as a -2.2 m displacement. The overall displacement is the sum of the positive (North) and negative (South) movements.  If the sum turns out to be negative, then the direction is opposite of North; that is, it would be South.

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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