Section 1 review
Position describes a location in space relative to an origin. Coordinates describe a position in three dimensions, using a set of three numbers (such as xy, and z) and a set of distance units (such as meters). An object’s position is a vector: a quantity with both a value (magnitude) and direction. Displacement is also a vector: It describes a change in position. Vectors can be added graphically (with the “head-to-tail” rule) or numerically—by separately adding their x-, y-, and z-components. Read the text aloud
position, origin, displacement, vector, magnitude, scalar, coordinates

Review problems and questions

  1. Classify each of the following as a distance or a displacement:
    1. Jodie sat 20 ft from the teacher’s desk.
    2. Maurice drove his car a quarter-mile north of the train station.
    3. Yasmin hiked 6 km through the San Gabriel Wilderness.
    4. Ali kicked the ball 40 yards away. Read the text aloud Show
  1. In one dimension, positions and displacements can be positive, negative, or zero.
    1. What is the difference between a negative position and a negative displacement?
    2. Is it possible to undergo a negative displacement and end up at a positive position? Read the text aloud Show
  1. A dog initially located at position (3, 3) m in the xy plane undergoes the following displacements: d1 = (2, 1) m, d2 = (−4, −2) m, and d3 = (3, −2) m.
    1. What is the total displacement of the dog?
    2. What is the final position of the dog with respect to the origin? Read the text aloud Show
  1. A plane starts at airport A and undergoes the following displacements before landing at airport B: d1 = (+14 km, +32 km) and d2 = (+18 km, −11 km). Next, the plane returns directly to airport A.
    1. What displacement does the plane undergo during the return trip?
    2. What is the total displacement of the plane during the entire round trip? Read the text aloud Show
What is the ball's displacement?
  1. Step i: A ball rolls from the origin on a one-dimensional coordinate axis and stops at (x = 30 m).
    Step ii: It next rolls from (x = 30 m) to (x = −30 m).
    Step iii: Finally, it rolls from (x = −30 m) to (x = 0 m).
    1. What is the ball’s displacement during Step i?
    2. What is the ball’s displacement during Step ii?
    3. What is the ball’s displacement during Step iii?
    4. What is the total of the three displacements?
    5. Generalize about the displacement of any round trip (one that begins and ends at the same position). Read the text aloud Show

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