Displacement Examples in Physics

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 m4 \text{ m} east and then 3 m3 \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\text{Distance} = 7 \text{ m}, \quad \text{Displacement} = 5 \text{ m at } 36.9° \text{ N of E}

First step

1
Total distance traveled is the sum of path lengths: d=4+3=7 md = 4 + 3 = 7 \text{ m}.

Full solution

  1. 2
    Displacement is the straight-line distance from start to finish: ∣d⃗∣=42+32=16+9=25=5 m|\vec{d}| = \sqrt{4^2 + 3^2} = \sqrt{16 + 9} = \sqrt{25} = 5 \text{ m}
  2. 3
    Direction: θ=tan⁡−1(34)≈36.9°\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 m400 \text{ m} circular track. What is the runner's displacement and total distance?

Example 3

medium
A hiker walks 88 m east then 66 m south. Find the magnitude and direction of the displacement.

Example 4

medium
A boat sails 55 km north, 1212 km east, then 55 km south. Find the magnitude of the displacement and the distance traveled.

Example 5

hard
A particle's position is x(t)=3t2−2tx(t) = 3t^2 - 2t m. Find the displacement between t=1t = 1 s and t=4t = 4 s.

Example 6

hard
A particle moves 2020 m at 30°30° above horizontal, then 1515 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 m100 \text{ m} north and then 100 m100 \text{ m} south. What is the displacement?

Example 2

medium
A hiker walks 3 km3 \text{ km} north, then 4 km4 \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=2x=2 m to x=10x=10 m. What is the displacement?

Example 4

easy
A car drives 55 km east then 55 km west, returning to start. What is its displacement?

Example 5

easy
An object moves from x=8x=8 m to x=3x=3 m. Find the displacement.

Example 6

easy
A walker goes 33 m north then 44 m north. What is the total displacement?

Example 7

easy
A ball is dropped and lands 55 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=−2x=-2 m an object moves to x=+6x=+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 66 m east then 88 m north. What is the magnitude of the displacement?

Example 12

medium
A car goes 99 km east, then 33 km west. Find the net displacement.

Example 13

medium
A path is 1212 m east then 55 m south. Find the displacement magnitude and compare to the distance travelled.

Example 14

medium
An elevator goes up 1010 m, down 44 m, up 22 m. Net vertical displacement (up positive)?

Example 15

medium
A boat sails 44 km north, 44 km east, 44 km south. Find the displacement from start.

Example 16

medium
A runner's position changes from x=4x=4 m to x=4x=4 m after a lap, but she ran 400400 m. Give displacement and distance.

Example 17

challenge
A drone flies 3030 m east, 4040 m north, then 3030 m west. Find the displacement magnitude.

Example 18

challenge
A particle's position is x(t)=t2x(t)=t^2 m. Find its displacement between t=1t=1 s and t=3t=3 s.

Example 19

challenge
Vectors: a walk is 77 m east then 2424 m north. Find the displacement magnitude and confirm it is a Pythagorean triple.

Example 20

medium
A car goes 55 m east, 55 m north, 55 m east. Find the displacement magnitude.

Example 21

medium
An object moves +10+10 m then −4-4 m then +1+1 m along a line. Find the net displacement.

Example 22

medium
A walk is 99 m north and 4040 m east. Find the displacement magnitude.

Example 23

easy
An object moves from x=−3x = -3 m to x=+4x = +4 m. Find the displacement.

Example 24

easy
A cyclist rides 200200 m east, then 200200 m east again. Find the displacement.

Example 25

easy
A car drives 5050 m east, then 8080 m west. Find the displacement (take east positive).

Example 26

easy
A child runs 55 m forward and 55 m back. What is the magnitude of the displacement?

Example 27

easy
From x=12x = 12 m, an object moves to x=2x = 2 m. State the displacement with sign.

Example 28

medium
A drone flies 1515 m east, 88 m north, then 99 m west. Find the magnitude of the displacement.

Example 29

medium
A particle's position is x(t)=5tx(t) = 5t m. Find its displacement from t=2t = 2 s to t=7t = 7 s.

Example 30

medium
From start, a vehicle goes 2020 m north then 2020 m east. Express the displacement vector in component form.

Example 31

medium
A car moves with vavg=+10v_{avg} = +10 m/s for 44 s. Find its displacement.

Example 32

medium
A particle starts at the origin and ends at (6,8)(6, 8) m. Find the magnitude and direction of the displacement.

Example 33

medium
Two displacement legs are a⃗=(3,4)\vec{a} = (3, 4) m and b⃗=(−3,4)\vec{b} = (-3, 4) m. Find the total displacement vector and its magnitude.

Example 34

hard
A particle moves with velocity v(t)=4−2tv(t) = 4 - 2t m/s. Find the displacement from t=0t = 0 to t=3t = 3 s.

Example 35

hard
A boat heads v⃗b=(4,0)\vec{v}_b = (4, 0) m/s in still water for 1010 s, with a current v⃗c=(0,3)\vec{v}_c = (0, 3) m/s. Find the boat's displacement.

Example 36

hard
A car goes 3030 m east in 55 s, then 5050 m west in 1010 s. Find the average velocity (with sign).

Example 37

hard
A plane flies 100100 km east, then 100100 km at 60°60° north of east. Find the magnitude of the total displacement.

Example 38

hard
A particle starts at (2,−3)(2, -3) m and ends at (−4,5)(-4, 5) m. Find the displacement vector and its magnitude.

Example 39

challenge
A car accelerates from rest at a=2a = 2 m/s2^2 for 55 s, then maintains its speed for 55 more seconds. Find the total displacement.

Example 40

challenge
A particle moves along a path: north 33 m, east 44 m, south 33 m, west 44 m. Find displacement and distance.
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Related Concepts

PositionVelocityVectors

Background Knowledge

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

position