Worksheet: Position, Displacement, and Distance

In this worksheet, we will practice differentiating between position, displacement, and distance involving using vector notation.

Q1:

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

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

Q2:

What kind of information does this signpost show?

  • Adistance
  • Bvelocity
  • Cdisplacement
  • Dspeed

Q3:

What is the name of the vector quantity which gives the total change of a particle’s position?

  • Adistance
  • Bacceleration vector
  • Cdisplacement
  • Dvelocity vector

Q4:

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)

Q5:

A particle moving in a straight line has a position vector r, defined by the relation rn=(𝑑+3), where 𝑑 is the time, measured in seconds, and n is a unit vector. Determine the magnitude of the displacement vector s in meters after 4 seconds.

Q6:

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

Q7:

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

Q8:

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

Q9:

A person rode a bicycle 7 km west and then 13 km 60∘ north of west. Find the total distance covered by the person.

Q10:

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

Q11:

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

Q12:

Given that a ship covered 300 m due west and then 675 m due north, determine its displacement, approximating its angle to the nearest minute.

  • A975 m, 662β€²βˆ˜ south of east
  • B75√97 m, 2358β€²βˆ˜ north of west
  • C75√97 m, 662β€²βˆ˜ north of west
  • D450 m, 2358β€²βˆ˜ north of east

Q13:

A bird leaves its nest and flies for 5 kilometers in the direction 60∘ north of east before stopping to rest in a tree. It then flies 10 kilometers southeast from the tree, landing on top of a telephone pole. Given that the vector (1,0) represents a displacement of 1 kilometer east and the vector (0,1) represents a displacement of 1 kilometer north, find the vector that represents the displacement of the telephone pole from the nest.

  • Aο€Ώ5√2+5√32,112βˆ’5√2
  • Bο€Ώ5√2+5√32,112+5√2
  • Cο€Ώ52+5√2,5√32βˆ’5√2
  • Dο€Ώ5√2+52,5√32βˆ’5√2
  • Eο€Ώ5√2+5√32,52+5√2

Q14:

A man walks from his house to a bank and then from the bank to a supermarket. Given that the displacement of the bank from his house is represented by the vector u and the displacement of the supermarket from the bank is represented by the vector v, what does the vector uv+ represent?

  • Athe displacement of the supermarket from the bank
  • Bthe displacement of the bank from the supermarket
  • Cthe total distance the man traveled to the supermarket
  • Dthe displacement of the man’s house from the supermarket
  • Ethe displacement of the supermarket from the man’s house

Q15:

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

  • ADisplacement
  • BDistance

Q16:

If you were lost in a forest, would you prefer to know your distance or your displacement from the nearest settlement?

  • Adistance
  • Bdisplacement

Q17:

The displacement of a particle of unit mass is given as a function of time by the relation si(𝑑)=ο€Ή35π‘‘βˆ’2π‘‘ο…οŠ¨, where i is constant unit vector, 𝑠 measured in centimeters , and 𝑑 in seconds. Given that the particle started its motion at 𝑑=0, find the total distance covered in the first 5 seconds of its motion.

Q18:

Mason and Amelia started walking from the same point. Mason walked 1 mile southwest and then 3 miles northwest. Amelia walked 3 miles northwest and then 1 mile southwest. What can you say about where they ended up?

  • AThey ended up 2 miles apart.
  • BThey ended up at the same place.
  • CThey ended up 4 miles apart.
  • DMason is west of Amelia.
  • EThey ended up 6 miles apart.

Q19:

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⟩

Q20:

A particle started moving along a straight line. At time 𝑑 (where 𝑑β‰₯0), its position relative to a fixed point is given by π‘Ÿ=2𝑑+4π‘‘βˆ’2. Determine all the possible value of 𝑑 at which π‘Ÿ=4.

  • A32
  • B2,3
  • C12,3
  • D2
  • E1

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