Excel in math and science.

Join using Facebook Join using Google Join using email

Forgot password? New user? Sign up

Existing user? Log in

Your answer seems reasonable. Find out if you're right!

That seems reasonable. Find out if you're right!

Join using Facebook Join using Google Join using email

Forgot password? New user? Sign up

Existing user? Log in

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

Show explanation

View wiki

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

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

Show explanation

View wiki

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}

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

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

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

Show explanation

View wiki

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(\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}}

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

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

Show explanation

View wiki

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

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

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

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

Show explanation

View wiki

by Brilliant Staff