# Tag Info

56

The question is especially relevant from a didactical point of view because one has to learn to distingish between energy (work) and momentum (quantity of motion). The kinematic property that is proportional to $v$ is nowadays called momentum, it is the "quantity of motion" residing in a moving object, it's definition is $p:= mv$. The change of momentum ...

56

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 ...

51

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

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 ...

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 ...

42

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 ...

33

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 ...

31

By special relativity, the energy needed to accelerate a particle (with mass) grow super-quadratically when the speed is close to c, and is ∞ when it is c. $$E = \gamma mc^2 = \frac{mc^2}{\sqrt{1 - (\text{“percent of speed of light”})^2}}$$ Since you can't supply infinite energy to the particle, it is not possible to get to 100% c. Edit: ...

30

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 ...

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 ...

29

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 ...

28

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 ...

26

Let me just throw in an intuitive explanation. You could re-phrase your question as: Why does velocity only increase as the square root of kinetic energy, not linearly? Well, drop a ball from a height of 1 meter, and it has velocity v when it hits the ground. Now, drop it from a height of 2 meters. Will it have a velocity of 2v when it hits the ground?...

26

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 ...

23

The reason is because the time taken for the two trips are different, so the average speed is not simply $\frac{v_1 + v_2}{2}$ We should go back to the definition. The average speed is always (total length) ÷ (total time). In your case, the total time can be calculated as \begin{align} \text{time}_1 &= \frac{120 \mathrm{miles}}{40 \mathrm{mph}} \...

22

The best way to solve it would be experimentally, by doing the run several times, with calibrated instrumentation by the roadside to measure your speed. The acceleration won't have been constant, so that's not an assumption we can use. Knowing the 0-60 time capability won't really help; it could be different when accelerating up hill, compared to on the ...

21

There is no maximum energy of a freely moving massive particle in special relativity. The relativistic energy of a particle of rest mass $m$ moving in your frame at speed $v$ is given by $E=\gamma m c^2$ where $\gamma = \frac{1}{\sqrt{1-(v/c)^2}}$. If you look closely at $\gamma$ you will see that it is not defined at $v=c$ ($c$ is the speed of light), and ...

20

You cannot tell moving with constant speed apart from standing still. This is the principle of Galilean relativity.

19

Ah, this gives me a chance to give a proper home to an analysis I first posted on Reddit. (I would much rather have first posted it here :-P) Mathematical derivation It all starts with a blog post I've written that comes very close to addressing the exact question you're asking. In the post, I calculated how fast an object would be moving after falling a ...

19

I would think an object can be invisible to a human if it moves so fast that, within the time it passes the field of view of the human, it reflects too little light to be detected visually (human vision has very high, but still limited sensitivity to light). On the other hand, if the object moves so fast in air, it will produce a lot of noise and probably ...

19

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 ...

17

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 ...

16

This scientific problem – well, a more general one – has been solved in the following paper: http://arxiv.org/abs/1204.0162 Because it's legal in my country to move backwards in time, I remember the future event – one minute from now – in which Andrew Gibson will mention that he has this paper hanging in his physics lounge. He will curse me. 11 minutes ...

16

They do, its just usually negligible in practice. There's also scattering because the particles are not all the same (H2O, N2, O2, etc.)--but that, too, is usually negligible. Its mainly because there are so many particles in a single wave. Consider that the wave must be extremely short before it becomes noticeable (megahertz).

15

Velocity does indeed have to be measured relative to something. We can measure our radial velocity relative to any other astronomical object we care to, by measuring Doppler shifts. But if you want to know our velocity "relative to the Universe as a whole" rather than relative to any one object, we have to be a bit careful to define our terms. Because the ...

15

You've seen the speed of light quoted as roughly $3*10^8\, \text{m/s}$, so the speed of light is very fast compared to one meter and one second. This is roughly a human walking speed, so your question could be interpreted as asking why light is few hundred million times faster than a walking speed. The speed people walk is rather anthropocentric, though. ...

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