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.

  • A 𝑑 = 2 8 c m , 𝑠 = 2 8 c m
  • B 𝑑 = 7 6 c m , 𝑠 = 7 6 c m
  • C 𝑑 = 5 2 c m , 𝑠 = 2 8 c m
  • D 𝑑 = 7 6 c m , 𝑠 = 2 8 c m

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).

  • A s i j ( 𝑑 ) = βˆ’ 5 βˆ’ 6
  • B s i j ( 𝑑 ) = ο€Ή βˆ’ 3 𝑑  + ( βˆ’ 4 𝑑 ) 
  • C s i j ( 𝑑 ) = ( βˆ’ 6 𝑑 ) βˆ’ 4
  • D s i j ( 𝑑 ) = ο€Ή βˆ’ 3 𝑑 βˆ’ 5  + ( βˆ’ 4 𝑑 ) 

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.

  • A 2 1 i
  • B 1 6 i
  • C βˆ’ 3 i
  • D 2 6 i
  • E 1 5 i

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.

  • A 7 5 √ 1 3 meters, 5 6 1 9 β€² ∘ north of east
  • B 7 5 √ 1 3 meters, 3 3 4 1 β€² ∘ north of west
  • C 375 meters, 5 6 1 9 β€² ∘ north of east
  • D 7 5 √ 6 meters, 5 6 1 9 β€² ∘ south of east
  • E 7 5 √ 6 meters, 3 3 4 1 β€² ∘ 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¨.

  • A 𝑑 = 3 7 . 5  c m , 𝑑 = 2 0 . 5  c m
  • B 𝑑 = 4 4 . 1  c m , 𝑑 = 3 1 . 5  c m
  • C 𝑑 = 3 1 . 5  c m , 𝑑 = 4 4 . 1  c m
  • D 𝑑 = 2 0 . 5  c m , 𝑑 = 3 7 . 5  c m

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.

  • A 975 m, 6 6 2 β€² ∘ south of east
  • B 7 5 √ 9 7 m, 2 3 5 8 β€² ∘ north of west
  • C 7 5 √ 9 7 m, 6 6 2 β€² ∘ north of west
  • D 450 m, 2 3 5 8 β€² ∘ 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.

  • A ο€Ώ 5 √ 2 + 5 √ 3 2 , 1 1 2 βˆ’ 5 √ 2 
  • B ο€Ώ 5 √ 2 + 5 √ 3 2 , 1 1 2 + 5 √ 2 
  • C ο€Ώ 5 2 + 5 √ 2 , 5 √ 3 2 βˆ’ 5 √ 2 
  • D ο€Ώ 5 √ 2 + 5 2 , 5 √ 3 2 βˆ’ 5 √ 2 
  • E ο€Ώ 5 √ 2 + 5 √ 3 2 , 5 2 + 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.

  • A r = ⟨ βˆ’ 4 1 , 1 8 , βˆ’ 6 3 ⟩
  • B r = ⟨ βˆ’ 4 9 , 0 , βˆ’ 4 5 ⟩
  • C r = ⟨ 4 9 , 0 , 4 5 ⟩
  • D r = ⟨ 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.

  • A 3 2
  • B 2 , 3
  • C 1 2 , 3
  • D2
  • E1

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