Lesson Worksheet: Position, Displacement, and Distance Mathematics

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

Q1:

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

  • ADisplacement
  • BDistance

Q2:

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

Q3:

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

Q4:

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

Q5:

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

Q6:

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

Q7:

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)

Q8:

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

Q9:

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

Q10:

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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