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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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by Brilliant Staff

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