Practice Displacement in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

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Quick Recap

The straight-line change in position from start to end, with both a distance and a direction.

Where you ended up relative to where you started—direction and distance combined.

Showing a random 20 of 50 problems.

Example 1

medium
A bird flies from (2,3)(2, 3) to (10,9)(10, 9), then to (2,9)(2, 9). What is its displacement from start to end?

Example 2

challenge
Explain why average velocity uses displacement, not distance, and what that implies for a round trip.

Example 3

easy
Distance traveled is 12 m but displacement is 8 m. Is this possible?

Example 4

medium
A car travels 2020 km east and then 1515 km north. Compute the displacement magnitude.

Example 5

challenge
A point moves on a circle of radius rr from angle θ1=0\theta_1 = 0 to θ2=π/2\theta_2 = \pi/2 (counterclockwise). Find its displacement magnitude in terms of rr.

Example 6

hard
A particle's position at time tt is r⃗(t)=(t,t2)\vec r(t) = (t, t^2). Find its displacement from t=1t = 1 to t=3t = 3.

Example 7

easy
A car drives 10 km north. What is the direction of its displacement?

Example 8

easy
A person walks 5 m east and then 5 m west. What is their displacement?

Example 9

medium
Why can two people who travel very different distances end up with the same displacement?

Example 10

easy
A point moves from (1,2)(1, 2) to (4,6)(4, 6). Write the displacement as a vector.

Example 11

medium
A point moves along the sides of a rectangle with vertices (0,0),(6,0),(6,4),(0,4)(0,0), (6,0), (6,4), (0,4), going around once. Find both the displacement and the total distance traveled.

Example 12

easy
You walk 5 m east, then 5 m west. What is your displacement?

Example 13

medium
You walk 8 m east, 6 m north, then 8 m west. Find your displacement vector and its magnitude.

Example 14

easy
A point starts at (0,0)(0,0) and is displaced by ⟨7,−24⟩\langle 7, -24 \rangle. Find its ending position and displacement magnitude.

Example 15

medium
A drone flies from (0,0)(0,0) to (3,4)(3,4) to (6,0)(6,0). Find its total displacement from start.

Example 16

easy
Is displacement a scalar or a vector?

Example 17

easy
A point moves from (0,0)(0,0) to (8,6)(8,6). Find its displacement magnitude.

Example 18

easy
A point starts at (2,3)(2, 3) and has displacement ⟨5,−1⟩\langle 5, -1 \rangle. Find its ending position.

Example 19

challenge
A particle moves along r⃗(t)=(cos⁡t,sin⁡t)\vec r(t) = (\cos t, \sin t) from t=0t = 0 to t=2πt = 2\pi. Compare the total distance traveled to the displacement.

Example 20

easy
Is displacement a vector or a scalar?
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