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Excel in math and science

Master concepts by solving fun, challenging problems.

It's hard to learn from lectures and videos

Learn more effectively through short, interactive explorations.

Used and loved by over 7 million people

Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.

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Classical Mechanics

Vector Kinematics

Concept Quizzes

Position Vectors
Different Representations of Vectors
Scalar multiplication of velocity vectors
Adding velocity vectors
Total displacement of a set of displacement vectors
Total displacement from velocity vectors
Problem solving with vector kinematics - beginners

Challenge Quizzes

Vector Kinematics: Level 2-3 Challenges
Vector Kinematics: Level 3-4 Challenges
Vector Kinematics: Level 4-5 Challenges

Position Vectors

A car at point $A$ on a straight road goes west for $20$ seconds, arriving at point $B$ which is $200$ m away from $A.$ The car then heads back to the east for $30$ seconds, arriving at point $C$ which is $800$ m away from $B.$ What is the displacement of the car from point $A$ ?

Assume that $+$ is east and $-$ is west.

-600 m -800 m +800 m +600 m

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by Brilliant Staff

One morning, you wake up and decide to take a jog through the town. You take $54 \text{ seconds}$ to run $250 \text{ m}$ straight north, then you turn right and take $42 \text{ seconds}$ to run $178 \text{ m}.$ Then you turn right again and run down the street for $9 \text{ seconds}$ covering $30 \text{ m}$ until you to stop. Assuming that the coordinates of your home are the origin $(0, 0),$ find the position vector of the place where you stop.

Take eastward as $+\hat{i}$ and northward as $+\hat{j} .$

178 \text{ m} \hat{i} - 220 \text{ m} \hat{j}

220 \text{ m} \hat{i} + 178 \text{ m} \hat{j}

178 \text{ m} \hat{i} + 280 \text{ m} \hat{j}

178 \text{ m} \hat{i} + 220 \text{ m} \hat{j}

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by Brilliant Staff

A soccer player undergoes two successive displacements: $\Delta \vec{r_A} = (28 \text{ m})\hat{i} + (8\text{ m})\hat{j} \text{ followed by } \Delta \vec{r_B} = (-28\text{ m}) \hat{i}+(7\text{ m}) \hat{j}.$ What is the total displacement of the soccer player?

15 \text{ m} \hat{i}

20 \text{ m} \hat{i} - 5 \text{ m} \hat{j}

30 \text{ m} \hat{i} - 5 \text{ m} \hat{j}

15 \text{ m} \hat{j}

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by Brilliant Staff

The motion of a creature in three dimensions can be described by the following equations for positions in $x, y$ and $z$ directions: $\begin{aligned} x(t)&=3t^2 + 6 \\ y(t)&=- t^2 + 3t - 2 \\ z(t)&= 3t + 1. \end{aligned}$ Find the position vector of the creature at $t = 3.$

( {33}, -2, {10})

( {36}, -6, {8})

( {28}, -6, {15})

( {38}, -5, {12})

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The Andromeda galaxy is a giant spiral cluster of stars whose mass is that of $300$ billion Suns. You can see it with the naked eye as a faint elongated cloud in the night sky. Inasmuch as it subtends an angle of $4.1^{\circ}$ and is known to be larger than our own galaxy [ $163 \times 10^3$ light-years (units of ly) in diameter for Andromeda as compared to $100 \times 10^3$ light-years for our galaxy], how far away is it in light-years?

An object subtends an angle if the rays that extend from the vertex of the angle touch the edges of the object.

1.7 \times 10^6 \text{ ly}

4.6 \times 10^6 \text{ ly}

5.9 \times 10^5 \text{ ly}

2.3 \times 10^6 \text{ ly}

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by Brilliant Staff

Excel in math and science

Master concepts by solving fun, challenging problems.

It's hard to learn from lectures and videos

Learn more effectively through short, interactive explorations.

Used and loved by over 7 million people

Learn from a vibrant community of students and enthusiasts, including olympiad champions, researchers, and professionals.

Excel in math and science

Master concepts by solving fun, challenging problems.

It's hard to learn from lectures and videos

Learn more effectively through short, interactive explorations.

Used and loved by over 7 million people

Learn from a vibrant community of students and enthusiasts, including olympiad champions, researchers, and professionals.

Vector Kinematics

Concept Quizzes

Challenge Quizzes

Position Vectors

Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.

Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.