Classical Mechanics

Vector Kinematics

Scalar multiplication of velocity vectors

         

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

The motion of a creature of mass 2 kg 2 \text{ kg} moving on a two dimensional plane can be described by the following equations: vx(t)=5t+2 (m/s)vy(t)=2t2 (m/s),\begin{aligned} v_x(t)&=5t + 2 \text{ (m/s)} \\ v_y(t)&=2t - 2 \text{ (m/s)}, \end{aligned} where vx(t)v_x(t) and vy(t)v_y(t) denote the velocities in the xx and yy directions, respectively. Find the creature's momentum vector at t=3 s t = 3 \text{ s} in unit-vector notation.

The motion of a creature of mass 6 kg 6 \text{ kg} on a two dimensional plane can be described by the following equations: ax(t)=4 m/s2ay(t)=1 m/s2,\begin{aligned} a_x(t)&= 4 \text{ m/s}^2 \\ a_y(t)&= -1 \text{ m/s}^2, \end{aligned} where ax(t)a_x(t) and ay(t)a_y(t) denote the accelerations in the positive directions of the xx-axis and yy-axis, respectively. If the creature is initially at rest, what is the creature's velocity vector at t=2 s t = 2 \text{ s} in unit-vector notation?

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

The motion of a creature of mass 6 kg 6 \text{ kg} on a two dimensional plane can be described by the following equations: vx(t)=t2+4 (m/s)vy(t)=3t1 (m/s),\begin{aligned} v_x(t)&=t^2 + 4\text{ (m/s)} \\ v_y(t)&=3t - 1 \text{ (m/s)}, \end{aligned} where vx(t)v_x(t) and vy(t)v_y(t) denote the velocities in the xx and yy directions, respectively. Find the creature's momentum vector at t=2 s t = 2 \text{ s} in unit-vector notation.

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