# Tag Info

1

Starting from position measurements $x[i]$ taken at times $t[i]$, the total distance travelled is given by $$d[i] = \sum_{j=0}^{i-1}\left|x[j+1] - x[j]\right|$$ or, equivalently $$d[i] = \sum_{j=0}^{i-1}\left|\Delta x[j]\right|$$ where $\Delta x[j] = x[j+1] - x[j]$. Note the absolute values in the sum formulas.

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The velocity is downward, and the acceleration is downward. Whatever direction you choose, if you start with a velocity of zero the sign of both will be the same (if you throw the feather down, it will decelerate - so the acceleration will the "up". I don't think that is intended here). Whether the floor or the hand is zero in the coordinate system doesn't ...

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Change of velocity is definitely -8m/s, according to vector summation. Magnitude of change of velocity is 8m/s. '-' sign indicates that the change is taking in the other direction,i.e. in the direction opposite to the initial direction. 4-4=0 is the change in speed , not velocity

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If you define your axes in such a way that the runner has a speed of 4m/s in the y direction in point A, the the velocity in point A is: $V_A = 4 \, \text{m/s} \, \hat{y} + 0 \, \text{m/s} \, \hat{x}$ Your runner must have a speed of -4m/s in the y direction in point B, you get the velocity: $V_B = -4 \, \text{m/s} \, \hat{y} + 0 \, \text{m/s} \, \hat{x}$ ...

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There is no $v$ component. I understand the source of confusion, and non-perpendicular coordinate system axes are only very rarely used in practise since each axis then is not uniquely defining their own direction but "overlaps" with the other directions. And at the same time the usual definitions of cosine and sine are not directly usable to find the ...

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on solving the equation the v=0 and u= (-500) according the equation the resolution in not in the quadrant of the resultant so the resolution is negative in this case. i think this is the answer if the second equation is not considered there are infinite possibilities

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The right hand rule is simply a mathematical convention. We use right handed coordinate systems. We could make the left hand rule true if we wanted to, but we would need to adapt our equations to the new convention.

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I think your confusion is arising from the fact that you are imagining operators as matrices. This is mostly fine, but in this case, the operator itself being a vector is what is causing the confusion - so let me elaborate. ${\bf A}$ is a vector of operators. For example $${\bf A} = \pmatrix{ A_1 \\ A_2 \\ A_3}$$ We can denote this collectively as $A_i$. ...

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Vectors are perfect for linear motion. But half of mechanics behavior is about angular motion. Also in various cases you can factor a scalar out of a vector, and it tells very convenient things. e.g. amplitude out of the oscillation. Or phase. Energy-wise stuff is then way more easy to right. Also maths objects you get in physics are not only scalar and ...

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Quantities like mass, energy, current etc. do not have any direction. They only have a magnitude and can hence only "scale" vector quantities which is why they are called scalers. For e.g. in linear momentum $p = mv$ the mass only scales the velocity vector. The direction of linear momentum is still in the direction of the velocity. This image below ...

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Use the right hand rule. Point your thumb in the direction of the current and your fingers will curl around the wire in the direction of the magnetic field. For current flowing from a to b: Your thumb points down and to the right. Your fingers will be to the left of the loop pointing downward. If you curl them around you will see that the magnetic field ...

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You can get the direction of the field without actually drawing it. The magnetic field of the current through the resistor is not just up or down. The field lines go in a circle around the resistor. You can use the right-hand rule to visualize which the way the lines go around, either clockwise or counterclockwise. If the current flows from $b$ to $a$, ...

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I only know of these: http://www.youtube.com/watch?v=LYNOGk3ZjFM (PERIMETER INSTITUTE RECORDED SEMINAR ARCHIVE) http://www.youtube.com/watch?v=b5VUnapu-qs&list=PLiUVvsKxTUr66oLF6Pzirc1EgSstMbRZR (Indian University of Technology Madras) The first two I recommend because they are simply the same courses as the one that you are attending. The following ...

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You have the momentum given by the vector: $\vec{p}=m\vec{v}$ $\vec{v}=$ being the velocity vector. Now if you integrate the momentum with respect to velocity then you have the integral: $\int\vec{p} \cdot d\vec{v}=m\int \vec{v} \cdot d\vec{v}$ Where $\vec{v} \cdot d\vec{v}$ is the dot(scalar) product between the two vectors $\vec{v}$ and $d\vec{v}$ ...

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I am not going to answer your question for you, as that would deprive you from learning the material. I can clear up a few things for you though. The mass is $2kg$ The Force is given as three component vectors in the x, y, z direction ($i,j,k$) It gives you its velocity is three component vectors as well. You are given Force, Velocity($V_i$), Mass, and ...

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A force is a vector acting along a line in space. It may act anywhere along the line and the end result will be the same (2nd paragraph). The reason pure forces act on lines is that if they move away from the line there will be a torque applied also and the resulting motion will not be the same. The line of action of a force is the locus of point where no ...

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Vectors are considered free (of location) and are the same if they have the same magnitude (length) and orientation. So a vector A in one coordinate system with origin O is the same as a vector A in another coordinate system with origin O* even if O* is moving (translational and/or rotational motion) with respect to O. However, the meaning of the vector ...

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