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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 ...


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 ...


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 ...


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 ...


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 ...


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} ...


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 ...


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 ...


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 ...


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 ...


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 ...


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 ...


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 ...


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 ...


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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