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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

Scalar multiplication of velocity vectors

A velocity vector $\vec{v}$ of magnitude $7.0 \text{ m/s}$ is directed south. What is the direction of the vector $-5.0 \vec{v}?$

east south north west

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by Brilliant Staff

The motion of a creature of mass $2 \text{ kg}$ moving on a two dimensional plane can be described by the following equations: $\begin{aligned} v_x(t)&=5t + 2 \text{ (m/s)} \\ v_y(t)&=2t - 2 \text{ (m/s)}, \end{aligned}$ where $v_x(t)$ and $v_y(t)$ denote the velocities in the $x$ and $y$ directions, respectively. Find the creature's momentum vector at $t = 3 \text{ s}$ in unit-vector notation.

\left( 34 \hat{i} + 8 \hat{j} \right) \text{ kg}\cdot\text{m/s}

\left( -34 \hat{i} + -8 \hat{j} \right) \text{ kg}\cdot\text{m/s}

\left( 29 \hat{i} + -7 \hat{j} \right) \text{ kg}\cdot\text{m/s}

\left( 14 \hat{i} + -3 \hat{j} \right) \text{ kg}\cdot\text{m/s}

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by Brilliant Staff

The motion of a creature of mass $6 \text{ kg}$ on a two dimensional plane can be described by the following equations: $\begin{aligned} a_x(t)&= 4 \text{ m/s}^2 \\ a_y(t)&= -1 \text{ m/s}^2, \end{aligned}$ where $a_x(t)$ and $a_y(t)$ denote the accelerations in the positive directions of the $x$ -axis and $y$ -axis, respectively. If the creature is initially at rest, what is the creature's velocity vector at $t = 2 \text{ s}$ in unit-vector notation?

(13 \hat{i} - 3 \hat{j}) \text{ m/s}

(8 \hat{i} - 2 \hat{j}) \text{ m/s}

(5 \hat{i} - 4 \hat{j}) \text{ m/s}

(14 \hat{i} - 6 \hat{j}) \text{ m/s}

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by Brilliant Staff

A ship sails on the $xy$ -plane in a direction that makes a $60 ^{\circ}$ angle with the positive direction of the $x$ -axis, at a speed of $27 \text{ m/s}.$ Find the velocity vector of this ship in unit-vector notation.

\displaystyle{ \left(13 \hat{i} + 13\sqrt{3} \hat{j} \right)\text{ m/s}}

\displaystyle{ \left( \frac{27}{2} \hat{i} + \frac{27 \sqrt{3}}{2} \hat{j}\right)\text{ m/s}}

\displaystyle{ \left(\frac{27\sqrt{3}}{2} \hat{i} + \frac{27}{2} \hat{j}\right)\text{ m/s}}

\displaystyle{ \left(\frac{13}{2} \hat{i} + \frac{13\sqrt{3}}{2} \hat{j}\right)\text{ m/s}}

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by Brilliant Staff

The motion of a creature of mass $6 \text{ kg}$ on a two dimensional plane can be described by the following equations: $\begin{aligned} v_x(t)&=t^2 + 4\text{ (m/s)} \\ v_y(t)&=3t - 1 \text{ (m/s)}, \end{aligned}$ where $v_x(t)$ and $v_y(t)$ denote the velocities in the $x$ and $y$ directions, respectively. Find the creature's momentum vector at $t = 2 \text{ s}$ in unit-vector notation.

\left( 30 \hat{i} +48 \hat{j} \right) \text{ kg}\cdot\text{m/s}

\left( 8 \hat{i} +30 \hat{j} \right) \text{ kg}\cdot\text{m/s}

\left( 40 \hat{i} +5 \hat{j} \right) \text{ kg}\cdot\text{m/s}

\left( 48 \hat{i} +30 \hat{j} \right) \text{ kg}\cdot\text{m/s}

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by Brilliant Staff