Displacement Examples in Physics: 46 Problems with Answers

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Displacement.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Physics.

Concept Recap

The change in position of an object, measured as the straight-line distance and direction from the starting point to the ending point.

How far you are from where you started, in a straight line. Not the path you took.

Read the full concept explanation →

How to Use These Examples

Read the first worked example with the solution open so the structure is clear.
Try the practice problems before revealing each solution.
Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: Displacement starts by naming what changes, over what time interval, and whether direction matters.

Common stuck point: Students often know a formula related to displacement but skip the recognition step: Am I describing motion over time with position, distance, direction, speed, velocity, or acceleration clearly separated? That leads to a correct-looking substitution attached to the wrong physical model.

Sense of Study hint: Ask: Am I describing motion over time with position, distance, direction, speed, velocity, or acceleration clearly separated?

Worked Examples

Example 1

easy

A person walks

4 \text{ m}

east and then

3 \text{ m}

north. What is the total distance traveled and the displacement?

Answer

Distance = 7 m, Displacement = 5 m at 36.9 ° N of E

First step

Total distance traveled is the sum of path lengths:

d = 4 + 3 = 7 \text{ m}

Full solution

2
Displacement is the straight-line distance from start to finish: $∣ \vec{d} ∣ = \sqrt{4^{2} + 3^{2}} = \sqrt{16 + 9} = \sqrt{25} = 5 m$
3
Direction: $\theta = \tan^{-1}\left(\frac{3}{4}\right) \approx 36.9°$ north of east.

Displacement is a vector quantity measuring the shortest path from start to end point, while distance is the total path length traveled. They differ whenever the path is not a straight line.

Example 2

medium

A runner completes one full lap around a

400 \text{ m}

circular track. What is the runner's displacement and total distance?

Example 3

medium

A hiker walks

8

m east then

6

m south. Find the magnitude and direction of the displacement.

Example 4

medium

A boat sails

5

km north,

12

km east, then

5

km south. Find the magnitude of the displacement and the distance traveled.

Example 5

hard

A particle's position is

x(t) = 3t^2 - 2t

m. Find the displacement between

t = 1

s and

t = 4

Example 6

hard

A particle moves

20

m at

30°

above horizontal, then

15

m horizontally. Find the displacement components and magnitude.

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

easy

A car drives

100 \text{ m}

north and then

100 \text{ m}

south. What is the displacement?

Example 2

medium

A hiker walks

3 \text{ km}

north, then

4 \text{ km}

east. What is the hiker's total distance walked and their displacement (magnitude and direction)?

Example 3

easy

A jogger runs from

x=2

m to

x=10

m. What is the displacement?

Example 4

easy

A car drives

5

km east then

5

km west, returning to start. What is its displacement?

Example 5

easy

An object moves from

x=8

m to

x=3

m. Find the displacement.

Example 6

easy

A walker goes

3

m north then

4

m north. What is the total displacement?

Example 7

easy

A ball is dropped and lands

5

m below the start (down positive). State the displacement.

Example 8

easy

A particle's displacement is given as '6 m'. What is missing to make it a complete vector statement?

Example 9

easy

From

x=-2

m an object moves to

x=+6

m. Find the displacement.

Example 10

easy

A drone returns to its launch pad after a tour. What is its displacement magnitude?

Example 11

medium

A hiker walks

6

m east then

8

m north. What is the magnitude of the displacement?

Example 12

medium

A car goes

9

km east, then

3

km west. Find the net displacement.

Example 13

medium

A path is

12

m east then

5

m south. Find the displacement magnitude and compare to the distance travelled.

Example 14

medium

An elevator goes up

10

m, down

4

m, up

2

m. Net vertical displacement (up positive)?

Example 15

medium

A boat sails

4

km north,

4

km east,

4

km south. Find the displacement from start.

Example 16

medium

A runner's position changes from

x=4

m to

x=4

m after a lap, but she ran

400

m. Give displacement and distance.

Example 17

challenge

A drone flies

30

m east,

40

m north, then

30

m west. Find the displacement magnitude.

Example 18

challenge

A particle's position is

x(t)=t^2

m. Find its displacement between

t=1

s and

t=3

Example 19

challenge

Vectors: a walk is

7

m east then

24

m north. Find the displacement magnitude and confirm it is a Pythagorean triple.

Example 20

medium

A car goes

5

m east,

5

m north,

5

m east. Find the displacement magnitude.

Example 21

medium

An object moves

+10

m then

-4

m then

+1

m along a line. Find the net displacement.

Example 22

medium

A walk is

9

m north and

40

m east. Find the displacement magnitude.

Example 23

easy

An object moves from

x = -3

m to

x = +4

m. Find the displacement.

Example 24

easy

A cyclist rides

200

m east, then

200

m east again. Find the displacement.

Example 25

easy

A car drives

50

m east, then

80

m west. Find the displacement (take east positive).

Example 26

easy

A child runs

5

m forward and

5

m back. What is the magnitude of the displacement?

Example 27

easy

From

x = 12

m, an object moves to

x = 2

m. State the displacement with sign.

Example 28

medium

A drone flies

15

m east,

8

m north, then

9

m west. Find the magnitude of the displacement.

Example 29

medium

A particle's position is

x(t) = 5t

m. Find its displacement from

t = 2

s to

t = 7

Example 30

medium

From start, a vehicle goes

20

m north then

20

m east. Express the displacement vector in component form.

Example 31

medium

A car moves with

v_{avg} = +10

m/s for

4

s. Find its displacement.

Example 32

medium

A particle starts at the origin and ends at

(6, 8)

m. Find the magnitude and direction of the displacement.

Example 33

medium

Two displacement legs are

\vec{a} = (3, 4)

m and

\vec{b} = (-3, 4)

m. Find the total displacement vector and its magnitude.

Example 34

hard

A particle moves with velocity

v(t) = 4 - 2t

m/s. Find the displacement from

t = 0

t = 3

Example 35

hard

A boat heads

\vec{v}_b = (4, 0)

m/s in still water for

10

s, with a current

\vec{v}_c = (0, 3)

m/s. Find the boat's displacement.

Example 36

hard

A car goes

30

m east in

5

s, then

50

m west in

10

s. Find the average velocity (with sign).

Example 37

hard

A plane flies

100

km east, then

100

km at

60°

north of east. Find the magnitude of the total displacement.

Example 38

hard

A particle starts at

(2, -3)

m and ends at

(-4, 5)

m. Find the displacement vector and its magnitude.

Example 39

challenge

A car accelerates from rest at

a = 2

m/s

^2

for

5

s, then maintains its speed for

5

more seconds. Find the total displacement.

Example 40

challenge

A particle moves along a path: north

3

m, east

4

m, south

3

m, west

4

m. Find displacement and distance.

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Related Concepts

Position Velocity Vectors

Background Knowledge

These ideas may be useful before you work through the harder examples.

position