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131

The acceleration along the track is always equal for every car, but for each car that acceleration aligns with the hills/gravity in different ways. As the front car crests a hill, the coaster is decelerating; the front car is being pulled backward by the other cars. But as the rear car crests a hill, it's being pulled forward by the rest of the cars. The ...


76

There is no controversy or ambiguity. It is possible to define mass in two different ways, but: (1) the choice of definition doesn't change anything about predictions of the results of experiment, and (2) the definition has been standardized for about 50 years. All relativists today use invariant mass. If you encounter a treatment of relativity that ...


74

[Caveat for this answer: it (both parts) is almost literally a transcript of a back-of-the-envelope calculation: there may be mistakes.] The calculation for a distant camera not co-rotating with the Earth A 50mm lens on 35mm film has about a 40 degree angle of view. Let's assume we're pointing that lens at the Earth so the Earth fills this angle of view, ...


61

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 home to work (defining my positive direction), then my velocity is positive if I go to work, but ...


52

Assuming you could get traction against the wall, you could run or walk up it at any speed. However, the problem is that for the large majority of circumstances, you cannot get traction against a vertical wall. The reason we can walk across the ground is because gravity pushes us downwards. This downward force is then opposed by an upward normal force from ...


46

The speed of sound in an ideal gas is given by $$a = \sqrt{\gamma R T}$$ Where $\gamma = \frac{C_p}{C_v}$, $R$ is the specific ideal gas constant and $T$ is the absolute temperature. Taking standard values for air, this makes a graph like this: The linear approximation is plotted by your formula, $a = 331\ \frac{m}{s}\ +\ 0.6 \frac{m}{sK} (T - 273\ K)$...


46

The maximum speed of an object that orbits the Sun at a certain distance $r$ is known as the escape velocity: $$ v_\text{esc} = \sqrt{\frac{2GM_\odot}{r}}, $$ where $M_\odot$ is the mass of the Sun. If the object would have a greater speed, it would eventually leave the solar system. So I'd say that the absolute maximum possible speed of any object in the ...


46

The speed of electricity is conceptually the speed of the electromagnetic signal in the wire, which is somewhat similar to the concept of the speed of light in a transparent medium. So it is normally lower, but not too much lower than the speed of light in the vacuum. The speed also depends on the cable construction. The cable geometry and the insulation ...


43

People already answered your question from a usefulness standpoint, but I just want to add that your reasoning isn't correct: Speed is usually defined as the magnitude of (instantaneous) velocity. So one could assume that average speed would be defined as the magnitude of average velocity. That's not how it works. If we have [speed] = [magnitude of ...


41

The notion of soft or hard object depends on the velocity of interaction. Water can be soft or hard as rock depending on how fast you fall in (or surf upon). For a shock, the main thing that matter is momentum. In space, where relative speeds can be very high, a simple bolt can cause serious damage to the ISS, and simple flakes of paint cause deep ...


38

Imagine the car stationary. The tire sits on the ground with the contact patch touching. As you start turning the wheel, the linkage to the wheels starts to rotate the contact patch on the ground. (There are also more complex motions because of the non-zero caster angle of the front wheel). This rotation is opposed by the static friction of the tire. ...


37

Let me start by clarifying that I assume the question is whether a superhuman or any object of human size can render itself invisible through speed alone. And that the speed of said object must be $v\ll c$. From this, I assume that the object or person being viewed must spend a reasonably long amount of time within the observer's field of view such that ...


37

The tricky part of this question is that you are given a graph of velocity but asked a question about speed. Several others have said essentially the same thing, but what really makes this clear for me is a graph of speed: The above is the graph of $$ y = \left \lvert 4 - \left ( \frac{x - 2}{2} \right ) ^2 \right \rvert \text{,}$$ which is just the ...


35

There are two reasons. The camera might just move at nearly the same speed as the Earth. In this case there is nearly no relative motion and the Earth looks nearly static. The second reason applies when the Earth has a high velocity relative to the camera - yet it is possible to get good images. What causes blur in the photo is not the speed of the object ...


35

I would like to add something to the already great answers posted. Obviously, non-relativistic is a qualitative term, you can translate it to "relativistic effects are so small that they're negligible in this problem". In the particular case you're talking about, and as was pointed out by Roger JBarlow and John Rennie, you can calculate the Lorentz factor ...


34

The complete answer to that question is an open problem in fluid mechanics, as exact closed form solutions to the irrotational surface gravity water wave equations are unknown. However, under certain asymptotic approximations, we can estimate the speed of these waves. Irrotational inviscid surface waves are governed by Laplace's equation, i.e. $$\nabla^2 ...


33

At the ambient temperature and pressure (assuming atmospheric pressure), the sound speed is pretty close to $340\ \frac{\text{m}}{\text{s}}$, and it seems (from internet research) that the first contender is about $16\ \text{m}$ further away from the guy firing the gun, which comes down to a delay of about $.05\ \text{s}$ in hearing the sound if the sound is ...


32

At high speeds the structure of the material becomes far less important than it is at low speeds. At high enough speeds, the issue is not whether the tomato can retain structure during the impact (it wont), but rather the issue becomes one of sheer mass. The issue is easiest to see in the tomato's reference frame, where one treats the tomato as holding ...


32

The definition of speed (please, let me call it velocity hereinafter) is not random at all. It seems you understand that it must depend on the distance $d$ and the time $t$, so I'll skip to the next stage. Evidently (for a constant $t$) velocity increases if $d$ does; and (for a constant space) $v$ decreases if $t$ rises. That constrains the ways we can ...


30

Is it fair to judge this speedskating race by only 3 thousands of a second? Yes, it's "fair". Not only is it according to the current rules of the event**, but also: There are at least three asymmetries that have far larger impact and are all considered "fair". They happen to start in different lanes (and must cross-over thereafter). That means they ...


30

In addition to Jim's answer, you could get enough traction if you are allowed to run up the wall with wings (airfoils). Formula 1 racecars could theoretically drive on the walls or ceilings without falling simply because the aerodynamic downforce generated by those wings can be up to 5 times its weight. Of course you'd have to run at superhuman speed in ...


30

I think that this question is why sound waves are non-dispersive whereas gravity waves on the surface of water are and also depend on the depth of the water. In fact if the depth of the water is less than about half a wavelength, the speed of the gravity waves is $\sqrt{gd}$ and not dependent on the wavelength of the waves. The speed of gravity waves ...


30

No. I assume you're thinking that a black hole made from light would have a zero rest mass and could therefore travel at the speed of light. However the rest mass of any black hole is due not only to the mass that went into it but also the energy (e.g. photons) that went into it. The increase in mass due to the energy is given by Einstein's famous equation $...


28

When we say a particle is non-relativistic we mean the Lorentz factor $\gamma$ is close to one, where $\gamma$ is given by: $$ \gamma = \frac{1}{\sqrt{1 - v^2/c^2}} $$ So saying $\gamma$ is close to one means that the velocity $v$ must be much less than $c$. With a bit of algebra we can show that the kinetic energy of a particle is given by: $$ T =(\...


27

It does, but the effects are negligible in the regions we think about. If you think about a volume of air as a box of atoms bouncing around, you can apply an oscillating pressure gradient across that box and show that it behaves close enough to an ideal wave propagation medium that you can get away with using such an ideal model. The variations you are ...


26

If you consider a rotating propeller, it has the following properties: you can see that something is there you cannot see what it is; you just happen to know it you cannot count the blades or really distinguish the features at all you cannot even tell the distance to the blurry "thing" in front of you people are known to walk into running propellers because ...


24

I will provide a bit more formal of an answer. "Speeding up" or "slowing down" typically refers to whether the speed of an object is increasing or decreasing. Imagine you are in a boat speeding down a canal (so that you may only move in one dimension - the canal is very narrow). At $t=2$, you flip a switch and your engine starts running in reverse. Here ...


23

Unsurprisingly this has been the subject of several scientific papers. In particular Google for papers by J. W. Glasheen and T. A. McMahon. They studied the basilisk lizard, but their results can be extrapolated to humans. It's debatable how reliable such a large extrapolation is, but the result is that the required speed is so far beyond human ability that ...


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