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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 cross-country skier moves 36 meters eastward, then 44 meters westward, and finally 22 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 Master-level, three-segment motion. There are two eastward movements and one westward movement. When it comes to the direction-ignorant distance quantity, these directions do not matter. Simply add up the length of the three movements and you have calculated the amount of ground that is covered

The quantity displacement is a direction-conscious quantity. Direction matters! Both eastward movements take the skier away from the starting position; they add together to give the skier an eastward displacement. But the westward movement partially negates this motion and takes the skier back towards the starting point (but not past it). Because the second movement is in the opposite direction as the other two movements, one must subtract this from the length of the two eastward segments.

A common approach for questions like these involves defining East as the positive direction and West as the negative direction. A 44-meter westward movement is thought of as a -44 m displacement. The overall displacement is the sum of two positive (East) and one 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 3-segment "Master"-level question ( like the 4-segment "Wizard" level questions) 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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