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One of the results of special relativity is that a particle moving at the speed of light does not experience time, and thus is unable to make any measurements. In particular, it cannot measure the velocity of another particle passing it. So, strictly speaking, your question is undefined. Particle #1 does not have a "point of view," so to speak. (More ...

21

The mass (the true mass which physicists actually deal with when they calculate something concerning relativistic particles) does not change with velocity. The mass (the true mass!) is an intrinsic property of a body, and it does not depends on the observer's frame of reference. I strongly suggest to read this popular article by Lev Okun, where he calls the ...

11

No. Any circular orbital velocity is about 70% ($1/\sqrt{2}$) of the required escape velocity. To find circular orbital velocity, equate the centripetal force to the force of gravity: $$\frac{m v^2}{r} = G \frac{ M m}{r^2} \rightarrow \boxed{ v_\textrm{circ} = \sqrt{\frac{GM}{r}}}$$ To find escape velocity, equate the magnitude of the potential energy to ...

10

Since the Lorentz transformations are a consequence of the postulate of constancy of the speed of light, together with some homogeneity and parallel postulates, it is a little difficult to make precise the request for a Lorentz-transformation free demonstration. But I will interpret the question as asking for a synthetic proof of the addition of velocities. ...

10

One's naive expectation would be that as the object moves through the medium, it collides with molecules at a rate proportional to $v$. The volume swept out in time $t$ is $A v t$, where $A$ is the cross-sectional area, so the mass with which it collides is $\rho A v t$. The impulse in each collision is proportional to $v$, and therefore the drag force ...

9

The complete relevant text in the book is The de Broglie wave equation relates the velocity of the electron with its wavelength, λ = h/mv ... However, the equation breaks down when the electron velocity approaches the speed of light as mass increases. ... Actually, the de Broglie wavelength should be $$\lambda = \frac hp,$$ where p is the ...

9

This is what special relativity is all about.. In special relativity you cannot simply state that particle 2 is moving at c+c=2c in a reference frame where particle 1 is at rest. Speeds add like this (easily found in wikipedia): $$v_2^{'} = \frac{v_1+v_2}{1+\frac{v_1v_2}{c^2}}$$ i.e. the speed of particle 2 $v_2'$ in a reference frame where particle 1 is ...

9

It's simpler than you (probably) think. In your example of defining speed: this is a change of position $s$ in a time $t$. The units of distance are metres and the units of time are seconds, so the units of velocity are metres per second. So far so good. Now consider acceleration: this is a change of velocity $v$ in a time $t$, so the units of acceleration ...

8

Instantaneous velocity can never be measured since there is no way in the real world to do anything instantaneously. All measurements take some amount of time to peform. For example the comment to the question mentioned using the Doppler effect to measure instantaneous velocity. That is not possible since to measure the frequency of a wave you have to ...

8

No, the escape velocity doesn't need to be maintained for any length of time. Escape velocity is the minimum speed you need to have at the Earth's surface to be able to escape the gravitational pull, without using a rocket or other continuous propulsion. In other words, ignoring all sources of gravity other than the Earth, if you launch a projectile ...

7

Terminal velocity is the maximum velocity that you can reach during free-fall. If you imagine yourself falling in gravity, and ignore air resistance, you would fall with acceleration $g$, and your velocity would grow unbounded (well, until special relativity takes over). This effect is independent of your mass, since $F = ma = mg \Rightarrow a = g$ Where ...

7

Here is a very basic estimation: The kinetic energy of a 1000 kg car moving at 60 km/h is $$E=\frac{mv^{2}}{2}=\frac{1000kg(16.7m/s)^{2}}{2}=138.9 kJ$$ The heat of gasoline combustion is 47 MJ/kg = 35000 kJ/litre. Assuming 10% efficiency of the car's engine, you would need to burn $$\frac{138.9 kJ}{0.1\cdot35000kJ/l}=0.04 litre$$ of gasoline to accelerate ...

7

I endorse Ron's answer – it's the systematic way to proceed. The velocity $v/c$ may be written as $\tanh \eta$ where $\eta$, the rapidity or whatever, is the hyperbolic (Minkowski) counterpart of the (Euclidean) angle. The addition of velocities then boils down to an addition formula for $\tanh(\eta_1+\eta_2)$ because the rapidities just add additively. Let ...

7

He "only" flew at the maximum speed of 370 m/s or so which is much less than the speed of the meteoroids – the latter hit the Earth by speeds between 11,000 and 70,000 m/s. So he was about 2 orders of magnitude slower. The friction is correspondingly lower for Baumgartner. Note that even if he jumped from "infinity", he would only reach the escape velocity ...

6

Attach a rope to a suitable part of the person's anatomy (*) Spin them around in a circle Use the accelerometers to measure the anglular velocity and hence the outward force, use the inclinometers to measure the angle of the rope to the vertical. Simple force diagram gives you the person's mass. If the reader is in a country with too many lawyers - I ...

6

No, and no. For several reasons: You do not need a calibrated measuring stick and clock to measure distance and time. You can pick up a random piece of wood and call that your length unit, and measure time using any convenient repetitive physical process, such as your pulse. (Of course a pulse does not make a particularly accurate clock, but just pretend ...

6

You should think of this by timestepping Newton's laws--- if you know the positions and velocity and one instant, you know the force, and the force determines the acceleration. This allows you to determine the velocity and an infinitesimal time in the future by $$v(t+dt) = v(t) + dt F/m$$ $$x(t+dt) = x(t) + dt v$$ You then find the position and ...

6

Suppose you throw a ball upwards at some velocity $v$. When you catch it again it's traveling downwards at (ignoring air resistance) a velocity of $-v$. So somewhere in between throwing and catching the ball it must have been stationary for a moment i.e. it's instaneous velocity was zero. Obviously this was at the top of it's travel. When you throw the ball ...

6

The distance between Earth and Alpha Centauri is $4.4\,\text{ly}$. Dividing by $60\,\text{years}$ it's approximately $22000\,\text{km/s}$. The relativistic factor (I mean $\gamma = \frac{1}{\sqrt{1-v^2/c^2}}$ for this is almost $1$. If we take a constant acceleration of $2g$ (it's possible) it would take only $320\,\text{hours}$ to reach this speed (and, ...

6

If you are not interested in relativistic effects, the answer to your question is easy to workout. According to Wikipedia, Alpha Centauri is 4.24 ly away (4.0114x$10^{16}\mathrm{m}$). So to get there in 60 years ($1892160000\mathrm{s}$). So your non-relativistic answer is $v = \frac{d}{t} = \frac{4.0114 \times 10^{16}}{1892160000} = 21200000 ... 6 We notice sudden changes in anything. We don't notice gradual change, whether in time or spread over space. If the car is moving uniformly along straight flat road, its acceleration a=0. Its velocity v is constant. When the brake pedal is pushed, friction causes the car to decelarate. a = some negative number. You can't avoid that. You want to ... 6 Short, short version: It's complicated. Slightly longer version: Internal combustion engines have at least two relevant performance characteristics: power and torque. Furthermore the maximum attainable values for both are functions of the current engine speed (RPM). Acceleration will cease if the current requirement for either power or torque equal the ... 6 Here's my guess: As you know, internal combustion engines burn fuel. The power output of the engine is a function of both the current RPM and the amount of fuel you inject. But there's a catch: the engine can burn a limited amount of fuel per cycle, and therefore the higher the RPM, the more fuel can be combusted. So (as @dmckee stated), at a given gear the ... 6 think about this with an example: the sine and cosine functions. They both average individually to zero over an interval. You can multiply those averages and still obtain zero. But if you multiply sin by itself and then average, you get a very distinct non-zero result. When the functions are arbitrary, the average of the product quantifies statistical ... 5 The article makes no sense. Einstein realized that matter was composed out of atoms, so the number of collisions of a Brownian particle with the surrounding molecule is finite in a finite period of time. However, for times$t$much longer than the typical scale between the collisions, the particle moves by a distance scaling like$\sqrt{t}\$. It follows that ...

5

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 ...

5

The thing you throw in the air is also traveling at the same speed you are, in the same direction. When you throw it up, it doesn't matter that the earth below is moving backwards at speed, nor that the moon is moving past even more quickly, nor that the earth itself is spinning and moving relative to the sun. The ball has a speed and direction and ...

5

The theory of relativity is often expressed as "Nothing can be faster than the speed of light". This is wrong. You can always define certain things that seem to "move" faster than the speed of light. For example, if you shine a laser pointer at the moon and wiggle it around, the little red dot on the moon's surface can "move" faster than the speed of ...

5

Have a look at http://en.wikipedia.org/wiki/Galilean_invariance. This is not too mathematical and explains what's going on. The basic idea is that there is no such thing as absolute motion. For example, because the earth is rotating as I sit here typing I'm moving at about 800 miles per hour. Why am I not splattered against my computer screen? It's because ...

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