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# Vector Kinematics

If you're in an Airbus 320 cruising at 600 mph, with a 150 mph crosswind, chances are you won't have a strong WiFi signal. Learn vector kinematics now, before you fly.

# 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 $$-5.0 \vec{v}?$$

The motion of a creature of mass $$2 \text{ kg}$$ moving on a two dimensional plane can be described by the following equations: \begin{align} v_x(t)&=5t + 2 \text{ (m/s)} \\ v_y(t)&=2t - 2 \text{ (m/s)}, \end{align} 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.

The motion of a creature of mass $$6 \text{ kg}$$ on a two dimensional plane can be described by the following equations: \begin{align} a_x(t)&= 4 \text{ m/s}^2 \\ a_y(t)&= -1 \text{ m/s}^2, \end{align} 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?

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.

The motion of a creature of mass $$6 \text{ kg}$$ on a two dimensional plane can be described by the following equations: \begin{align} v_x(t)&=t^2 + 4\text{ (m/s)} \\ v_y(t)&=3t - 1 \text{ (m/s)}, \end{align} 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.

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