Sort position, velocity, direction, coordinates, displacement and distance between same or different in each coordinate system
Added by Matthew A.
Step 1
In 2D Cartesian: r = (x, y); in 3D Cartesian: r = (x, y, z). - Velocity: the time derivative of position, v = dr/dt. In components, v = (dx/dt, dy/dt, dz/dt). - Direction: the orientation of the velocity or displacement, given by a unit vector in the direction of Show more…
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One of the difficulties in studying mechanics is that many common words are used with highly specific technical meanings, among them velocity, acceleration, position, speed, and displacement. The series of questions in this problem is designed to get you to try to think of these quantities like a physicist. Consider a physical situation in which a particle moves from point A to point B. This process is described from two coordinate systems that are identical except that they have different origins. The ________ of the particle at point A differ(s) as expressed in one coordinate system compared to the other, but the ________ from A to B is/are the same as expressed in both coordinate systems. Answer the questions in this problem using words from the following list: A. position B. direction C. displacement D. coordinates E. velocity F. acceleration G. distance H. magnitude I. vector J. scalar K. components
Adi S.
A particle undergoes three successive displacements in a plane, as follows: $vec{d}_{1}, 4.00 mathrm{m}$ southwest; then $vec{d}_{2}, 5.00 mathrm{m}$ east; and finally $vec{d}_{3}, 6.00 mathrm{m}$ in a direction $60.0^{circ}$ north of east. Choose a coordinate system with the $y$ axis pointing north and the $x$ axis pointing east. What are (a) the $x$ component and (b) the $y$ component of $vec{d}_{1}$ What are (c) the $x$ component and $(mathrm{d})$ the $y$ component of $vec{d}_{2} ?$ What are (e) the $x$ component and $(mathrm{f})$ the $y$ component of $vec{d}_{3}$ ? Next, consider the net displacement of the particle for the three successive displacements. What are (g) the $x$ component, (h) the $y$ component, (i) the magnitude, and (j) the direction of the net displacement? If the particle is to return directly to the starting point, (k) how far and ( 1 ) in what direction should it move?
Linda W.
A particle undergoes three successive displacements in a plane, as follows: $\vec{d}_{1}, 4.00 \mathrm{m}$ southwest; then $\vec{d}_{2}, 5.00 \mathrm{m}$ east; and finally $\vec{d}_{3}, 6.00 \mathrm{m}$ in a direction $60.0^{\circ}$ north of east. Choose a coordinate system with the $y$ axis pointing north and the $x$ axis pointing dinate system with the $y$ axis pointing north and the $x$ axis pointing east. What are (a) the $x$ component and (b) the $y$ component of $\vec{d}_{1}$ What are (c) the $x$ component and $(\mathrm{d})$ the $y$ component of $\vec{d}_{2} ?$ What are (e) the $x$ component and $(\mathrm{f})$ the $y$ component of $\vec{d}_{3}$ ? Next, consider the net displacement of the particle for the three successive displacements. What are (g) the $x$ component, (h) the $y$ component, (i) the magnitude, and (j) the direction of the net displacement? If the particle is to return directly to the starting point, (k) how far and ( 1 ) in what direction should it move?
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