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3

I know this is an old thread, but I had to figure this out for a problem on my physics homework. What helped me to understand this is to think about 2 objects on a spinning disk, one being close to the center of the disk and one being close to the outside of the disk. Angular (rotation) speed deals strictly with the angle. How long does each object take to ...


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We can call the first object P, and the second object Q. Then we can say that the location of the particles can be notated as $ <P_x, P_y>, <Q_x, Q_y> $ Therefore, the distance, $d$, between A and B is $d=\sqrt{(A_x-B_x)^2+(A_y-B_y)^2}$. So, because $x(t)=v_x*t+x(0)$, and $v=<U_1*\frac{B_x-A_x}{d},U_1*\frac{B_y-A_y}{d}>$ Combining all ...


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I think t=2s is not a wrong thing. Most of the questions have like, this and this happened at t=2s


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I know light's speed in vacuum is constant Correct. Specificly, we speak of "vacuum" (and evaluate "refractive index" value $n = 1$) in the context of signal exchange if phase speed and group speed of the "signal carrier" are equal to the signal front speed $c_0$; where $c_0$ is just a particular (non-zero) symbol which appears in the chrono-geometric ...


3

In a very real sense, the velocity of a light ray in a curved spacetime is constant, or at least as constant as it can be; this is because it follows a special path in spacetime called a geodesic. The problem with defining a "constant" vector on a curved surface (the surface of the Earth, say) is that you can't easily compare tangent vectors at two ...


2

Yes light does have different directions in different frames. Two observers with different velocities will see the same photon traveling in different directions. One observer standing still at noon sees light traveling vertically downward. Light that strikes the top of his head would also strike his toes. An observer running forward see light slanted ...


0

I know light's speed in vacuum is constant, but what about its velocity? The speed of light in vacuum is not constant, and because of this light curves, hence its vector-quantity velocity varies. Have a look at the Einstein digital papers and you can find Einstein talking about it: This is what John Rennie was referring to. Think about the room you're ...


7

Light can obviously travel in any direction, but the magnitude of its velocity (in vacuum) is always $c$. The magnitude of the velocity is a scalar i.e. just a number, but the velocity is a vector. To specify the velocity we need to choose some axes. For example I might choose the Cartesian axes $x$, $y$ and $z$. In that case light approaching me from the ...


3

Your equation is not valid, see Figure below With equations \begin{equation} \Vert\mathbf{r}\Vert^{2}=\mathbf{r}\circ \mathbf{r} \Longrightarrow 2\cdot \Vert\mathbf{r}\Vert\cdot d\Vert\mathbf{r}\Vert =2\cdot\left(\mathbf{r}\circ d\mathbf{r}\right)\Longrightarrow d\Vert \mathbf{r}\Vert =\dfrac{\mathbf{r}}{\Vert\mathbf{r}\Vert}\circ d \mathbf{r} \tag{01} ...


0

is $\left|\frac{d\vec{r}}{dt}\right| = \frac{d|\vec{r}|}{dt} $ [?] There's a subtlety here ... It depends on how (you want that) the right-hand side of your suggested equation is interpreted. We know, of course, by to the rigorous definition of what the notation you've used is supposed to mean, that the value of a derivative is evaluated "at" a ...


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When we say the velocity of the object at t=2sec is x m/s we mean from that point where the time t=0.


3

Actually you're asking two different questions. Is the magnitude of instantaneous velocity the same as instantaneous speed? Well, yes, that's the definition of instantaneous speed. Is this equation true? $$\biggl\lvert\frac{\mathrm{d}\vec{r}}{\mathrm{d}t}\biggr\rvert = \frac{\mathrm{d}\lvert\vec{r}\rvert}{\mathrm{d}t}$$ No, it's not - but instantaneous ...


1

Obviously not: think to a very simple (2d) example, $r(t)=(t,t)$. Componentwise, the derivative yields $1,1$, and hence $\lvert dr/dt\rvert=\sqrt{2}$. On the other hand, $\lvert r(t)\rvert = \sqrt{2}\lvert t \rvert$. And the absolute value function is not differentiable in zero. Hence the two derivative functions coincide almost everywhere, but not in ...


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Surely this just depends on the potential well in which the particle finds itself. If the function you describe is the solution of the equation of motion, then that will indeed be the motion of the particle. The function you wrote will give rise to a path that "never ends" - the particle keeps slowing down, but never stops. Of course in practice there are ...


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In the computer language FORTH the turtle can go anywhere in the plane, going always 'ahead' X units and turning left or right by a Y angle units. The turtle ignores the notion of negative and yet it moves i.e. in any referential the space coordinates vary in time , and it has a velocity. The Question and several of the Answers do not know the difference ...


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I will only consider one dimensional motion(motion along a single axis).The main objective of terms like position and velocity is to describe the motion of an object easily. We define velocity to be the rate of change of position .By convention we choose a fixed point (along the axis of motion) and call it origin and define an object's position on that line ...


6

From the math point of view, you cannot have “negative velocity” in itself, only “negative velocity in a given direction”. The velocity is a 3-dimension vector, there is no such thing as a positive or negative 3D vector. However, if you consider the velocity in direction $\mathrm{x}$, where $\hat{\mathbf{e}}_{\mathrm{x}}$ is some ...


1

I think one of the main reasons that you have velocity is to isolate a particular direction of movement from your forward speed. If you travel North north east, you can extract the speed at which you move eastwards by calculating your eastwards velocity (possibly 1/3 of your speed travelling NNE). Negative velocities probably arrived as a consequence of ...


4

Short: Given enough assumptions to make the question answerable. Feather size: Probably 300 to 500 mm for a small percentage of the feathers and closer to 50% of that for the majority Power and force: Without a complex analysis of flapping flight (with takeoff mode, soaring versus "hovering" capabilities and more) a definitive answer would be ...


55

Velocity is a vector. Speed is its magnitude. Position is a vector. Length (or distance) is its magnitude. A vector points in a direction in space. A negative vector (or more precisely "the negative of a vector") simply points the opposite way. If I drive from my home to my workplace (and then defining my positive direction in that way), then my velocity ...


1

The acceleration is the time derivative of the velocity: $$ a = \frac{dv}{dt} $$ so if the velocity does not change with time the acceleration is necessarily zero. Since in your example the velocity is constant during the interval that means $dv/dt = 0$ and therefore that $a = 0$ during the interval. The velocity doesn't have to be zero. Any constant ...


0

The relationship between wavelength and distance is similar to the relationship between frequency and duration, and no: neither pair is the same. You can see by using dimensional analysis. Wavelength is distance divided by cycles. Frequency is cycles divided by time. Multiply the two, the cycles cancel out, and you get distance divided by time, or velocity. ...


1

I am more familiar with graphing in Python than in the language you are using. The following snippet of code produces the graph you are asking for: import numpy as np import matplotlib.pyplot as plt # sci fi velocity graph D = 160934400000 # m v_i = 3070 # m/s total_time = 40*3600 # seconds: 40 hours # to cover half the distance in half the ...


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Velocity is a more widely used term, usable for all moving objects and waves, while wavelength is of course only usable for waves. Wavelength is the minimal distance between two points of a wave with the same phase. Take for example a sinusoidal wave: the wavelength will be the difference between two maxima or two minima. The velocity of a wave is used ...


1

A wavelength is a particular distance, corresponding to the length travelled during a period, which is a special time. Since $v=d/t$ holds good for the distance $d$ travelled by a constant velocity object over any given time interval $t$, a fortiori this relationship holds for the special, particular time known as the period. So, yes, $v=d/t$ is how you ...


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The lambda is the distance between 2 points having the same phase like two successive crests the velocity is the wave can be conceived as how many crests for example passes through a reference in a given time you can use both equations but c=f*lambda is used if you have lambda , its proof is V = distance / time , if a crest traveled a distance = wavelength ...


2

As the equations of motion are of second order, the higher derivatives give no new information (but follow uniquely from the initial conditions of position and velocity), therefore they usually are not discussed. (Note: As Timaeus pointed out there are specific scenarios, e.g. Norton's dome where intial values for the higher order derivates will change the ...



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