Vector Kinematics
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.