Lesson Worksheet: Position, Displacement, and Distance Mathematics

In this worksheet, we will practice differentiating between position, displacement, and distance traveled, including problems that use vector notation.


You traveled 213 miles from California to San Francisco. Does the β€œ213 miles” represent distance or displacement?

  • ADisplacement
  • BDistance


Using the given figure, calculate the distance, 𝑑, covered by a body that moves from point 𝐴 to point 𝐢 then returns to point 𝐡 and its displacement, 𝑠.

  • A𝑑=28cm, 𝑠=28cm
  • B𝑑=76cm, 𝑠=76cm
  • C𝑑=52cm, 𝑠=28cm
  • D𝑑=76cm, 𝑠=28cm


A person ran 160 mΒ east and then 175 mΒ north. Find the total distance covered by the person.


A car moved 150meterseast and then 225metersnorth. Find the magnitude and direction of its displacement, rounding the angle to the nearest minute.

  • A75√13 meters, 5619β€²βˆ˜north of east
  • B75√13 meters, 3341β€²βˆ˜north of west
  • C375 meters, 5619β€²βˆ˜north of east
  • D75√6 meters, 5619β€²βˆ˜south of east
  • E75√6 meters, 3341β€²βˆ˜north of east


According to the figure, a body moved from 𝐴 to 𝐡 along the line segment 𝐴𝐡, and then it moved to 𝐢 along 𝐡𝐢. Finally, it moved to 𝐷 along 𝐢𝐷 and stopped there. Find the distance covered by the body π‘‘οŠ§ and the magnitude of its displacement π‘‘οŠ¨.

  • A𝑑=37.5cm, 𝑑=20.5cm
  • B𝑑=44.1cm, 𝑑=31.5cm
  • C𝑑=31.5cm, 𝑑=44.1cm
  • D𝑑=20.5cm, 𝑑=37.5cm


A particle started moving in a straight line. After 𝑑 seconds, its position relative to a fixed point is given by π‘Ÿ=ο€Ήπ‘‘βˆ’4𝑑+7𝑑β‰₯0.m, Find the displacement of the particle during the first five seconds.

  • A5 m
  • B6 m
  • C40 m
  • D12 m


If the position vector of a body at time 𝑑 is given by rij(𝑑)=ο€Ήβˆ’3π‘‘βˆ’5+(βˆ’4π‘‘βˆ’6), find its displacement s(𝑑).

  • Asij(𝑑)=βˆ’5βˆ’6
  • Bsij(𝑑)=ο€Ήβˆ’3𝑑+(βˆ’4𝑑)
  • Csij(𝑑)=(βˆ’6𝑑)βˆ’4
  • Dsij(𝑑)=ο€Ήβˆ’3π‘‘βˆ’5+(βˆ’4𝑑)


The position vector of a particle relative to the point 𝑂 is given by the relation ri=(𝑑+4π‘‘βˆ’5), where i is a fixed unit vector and 𝑑 is the time. Find the displacement of the particle after 3 seconds.

  • A21i
  • B16i
  • Cβˆ’3i
  • D26i
  • E15i


A moving particle has a position vector r given by the relation rij(𝑑)=(6π‘‘βˆ’4)+(9𝑑+4), where i and j are the unit vectors. Find the magnitude of the particle’s displacement during the interval 2 to 6 seconds.

  • A24√13
  • B12√13
  • C20√5
  • D36√17
  • E40√5


Using point (4,9,βˆ’9) and direction vector βŸ¨βˆ’5,1,βˆ’6⟩, give the position vector r of the point on this line corresponding to parameter 𝑑=9.

  • Ar=βŸ¨βˆ’41,18,βˆ’63⟩
  • Br=βŸ¨βˆ’49,0,βˆ’45⟩
  • Cr=⟨49,0,45⟩
  • Dr=⟨4,9,βˆ’9⟩

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