Worksheet: Distance and Displacement

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In this worksheet, we will practice differentiating between distance and displacement and finding them.

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?

  • Aspeed
  • Bdistance
  • Cvelocity
  • Ddisplacement

Q3:

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

  • Avelocity vector
  • Bdistance
  • Cacceleration vector
  • Ddisplacement

Q4:

If the position vector of a body at time 𝑑 is given by r i j ( 𝑑 ) = ο€Ή βˆ’ 3 𝑑 βˆ’ 5  + ( βˆ’ 4 𝑑 βˆ’ 6 )  , find its displacement s ( 𝑑 ) .

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

Q5:

A particle moving in a straight line has a position vector r , defined by the relation r n = ( 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 r i = ( 𝑑 + 4 𝑑 βˆ’ 5 )  , where i is a fixed unit vector and 𝑑 is the time. Find the displacement of the particle after 3 seconds.

  • A 1 5 i
  • B 1 6 i
  • C 2 6 i
  • D 2 1 i
  • E βˆ’ 3 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€Ή 𝑑  βˆ’ 4 𝑑 + 7  m , 𝑑 β‰₯ 0 . Find the displacement of the particle during the first five seconds.

  • A 40 m
  • B 6 m
  • C 12 m
  • D 5 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  6 0 ∘ north of west. Find the total distance covered by the person.

Q10:

A car moved 1 5 0 m e t r e s east and then 2 2 5 m e - north. Find the magnitude and direction of its displacement, rounding the angle to the nearest minute.

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

Q11:

According to the figure, a body moved from 𝐴 to 𝐡 along the line segment 𝐴 𝐡 , and then it moved to 𝐢 along 𝐡 𝐢 . Finally, it moved to 𝐷 along 𝐢 𝐷 and stopped there. Find the distance covered by the body 𝑑  and the magnitude of its displacement 𝑑  .

  • A 𝑑 = 3 7 . 5  c m , 𝑑 = 2 0 . 5  c m
  • B 𝑑 = 3 1 . 5  c m , 𝑑 = 4 4 . 1  c m
  • C 𝑑 = 2 0 . 5  c m , 𝑑 = 3 7 . 5  c m
  • D 𝑑 = 4 4 . 1  c m , 𝑑 = 3 1 . 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 450 m, 2 3 5 8 β€² ∘ north of east
  • C 7 5 √ 9 7 m, 2 3 5 8 β€² ∘ north of west
  • D 7 5 √ 9 7 m, 6 6 2 β€² ∘ north of west

Q13:

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

  • A
  • B
  • C
  • D
  • E

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 u v + represent?

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

Q15:

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

  • ADistance
  • BDisplacement

Q16:

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

  • Adisplacement
  • Bdistance

Q17:

The displacement of a particle of unit mass is given as a function of time by the relation s i ( 𝑑 ) = ο€Ή 3 5 𝑑 βˆ’ 2 𝑑   , 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 6 miles apart.
  • BThey ended up 2 miles apart.
  • CMason is west of Amelia.
  • DThey ended up at the same place.
  • EThey ended up 4 miles apart.

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