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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.

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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?

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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.

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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.

Excel in math and science

Master concepts by solving fun, challenging problems.

It’s hard to learn from lectures and videos

Learn more effectively through short, conceptual quizzes.

Our wiki is made for math and science

Master advanced concepts through explanations,
examples, and problems from the community.

Used and loved by 4 million people

Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.

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