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Lesson: Distance and Displacement

In this lesson, we will learn how to differentiate between distance and displacement and how to find them.

Sample Question Videos

01:30

Worksheet • 17 Questions • 1 Video

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 = 7 6 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 = 2 8 c m , 𝑠 = 2 8 c m

Q2:

A particle moving in a straight line has a position vector ⃑ π‘Ÿ , defined by the relation ⃑ π‘Ÿ = ( 𝑑 + 3 ) ⃑ 𝑛 2 , where 𝑑 is the time, measured in seconds, and ⃑ 𝑛 is a unit vector. Determine the magnitude of the displacement vector ⃑ 𝑠 in metres after 4 seconds.

Q3:

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 7 5 √ 9 7 m, 6 6 2 β€² ∘ north of west
  • 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 975 m, 6 6 2 β€² ∘ south of east

Q4:

What kind of information does this signpost show?

  • Adisplacement
  • Bdistance
  • Cvelocity
  • Dspeed

Q5:

The position vector of a particle relative to the point 𝑂 is given by the relation ⃑ π‘Ÿ = ( 𝑑 + 4 𝑑 βˆ’ 5 ) ⃑ 𝑖 2 , 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 βˆ’ 3 ⃑ 𝑖
  • C 1 6 ⃑ 𝑖
  • D 2 6 ⃑ 𝑖
  • E 1 5 ⃑ 𝑖

Q6:

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

Q7:

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.

Q8:

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

  • Adistance
  • Bdisplacement

Q9:

The displacement of a particle of unit mass is given as a function of time by the relation ⃑ 𝑠 ( 𝑑 ) = ο€Ή 3 5 𝑑 βˆ’ 2 𝑑  ⃑ 𝑖 2 , where ⃑ 𝑖 is constant unit vector, 𝑠 measured in centimetres, 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.

  • A 181.25 cm
  • B 28.12 cm
  • C 278.12 cm
  • D 141.25 cm

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

Q11:

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

Q12:

A particle started moving in a straight line. After 𝑑 seconds, its position relative to a fixed point is given by Find the displacement of the particle during the first five seconds.

  • A 5 m
  • B 6 m
  • C 12 m
  • D 40 m

Q13:

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

Q14:

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 = 4 4 . 1  c m , 𝑑 = 3 1 . 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 = 3 7 . 5  c m , 𝑑 = 2 0 . 5  c m

Q15:

If the position vector of a body at time 𝑑 is given by ⃑ π‘Ÿ ( 𝑑 ) = ο€Ή βˆ’ 3 𝑑 βˆ’ 5  ⃑ 𝑖 + ( βˆ’ 4 𝑑 βˆ’ 6 ) ⃑ 𝑗 2 , find its displacement ⃑ 𝑠 ( 𝑑 ) .

  • A ⃑ 𝑠 ( 𝑑 ) = ο€Ή βˆ’ 3 𝑑  ⃑ 𝑖 + ( βˆ’ 4 𝑑 ) ⃑ 𝑗 2
  • B ⃑ 𝑠 ( 𝑑 ) = ( βˆ’ 6 𝑑 ) ⃑ 𝑖 βˆ’ 4 ⃑ 𝑗
  • C ⃑ 𝑠 ( 𝑑 ) = ο€Ή βˆ’ 3 𝑑 βˆ’ 5  ⃑ 𝑖 + ( βˆ’ 4 𝑑 ) ⃑ 𝑗 2
  • D ⃑ 𝑠 ( 𝑑 ) = βˆ’ 5 ⃑ 𝑖 βˆ’ 6 ⃑ 𝑗

Q16:

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

  • Adisplacement
  • Bdistance
  • Cacceleration vector
  • Dvelocity vector

Q17:

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

  • ADisplacement
  • BDistance
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