Cap'n Refsmmat

72 kilometers. The numbers? They're in there: [imath](-\infty, \infty)[/imath]. Why?

200 meters. You could try the math yourself if you'd like.

20m. I already answered that.

20m. From the train's frame: The train is stationary. The ball is moving 20m/s away. From the ball's frame: The ball is stationary. The train is moving at 20m/s away from the ball. From the station's frame: The train is moving at 20m/s away from the ball. The ball is stationary. They all are equally valid and give you the same answer to your question. That's the point I'd like to illustrate: all the frames are equally valid.

Because the ball is not in motion -- compared to the train. The relative velocity is 0m/s. And the train's velocity is only 20m/s compared to the Earth. You prefer using the Earth as a reference frame, but it's just as allowable to use the train.

By "not accelerating" you mean the speed of rotation is constant, I presume. But the metal of whatever object you're spinning undergoes constant acceleration while it rotates -- acceleration is a change in velocity, and velocity includes distance. As the metal revolves around the central axis its direction is constantly changing.

You are making this complicated, so: I passed out under the forces of launch (low blood pressure, it runs in my family) and woke up a few hours later. It doesn't matter anyway. I could just as easily say I started from a negative velocity and accelerated to zero velocity as I could say I started at zero velocity and accelerated to a positive one. It works either way.

0 N.

I didn't say I know I was in motion. (And if I did, ignore it.) All I said is that I know I'm in space in a box. It's impossible to tell if I'm in motion or now.

Using what reference frame? I don't understand the question.

Motor Daddy: You meant megalomaniac, but whatever. Every object is in motion relative to what? Other objects? If I'm flying through space in a solid box with no windows, I have no clue if I'm moving or not. There's no way of telling. So I can consider myself stationary and all the laws of physics will work. Every test I perform inside my box will say I'm stationary. If I put in a window and see the stars moving past I can say that they're moving and I'm stationary. I mean, how can you tell the difference? You can do the math for assuming you're stationary and everything else is moving and you'll find that it works out just fine.

That doesn't stop me. Read the tutorial I linked to and you'll see why it works. (Derivatives work via limits.) And why are they mistaken?

Yup.

Yes. If I have an equation describing the motion of an object, such as this: x = 20t I can find the velocity at any point in time by taking its derivative: v = 20 The instantaneous velocity is 20 m/s. http://www.scienceforums.net/forum/showthread.php?t=31921

You clearly aren't familiar with calculus.

Because the velocity relative to the train could be greater. I answered using the reference frame of the tracks. There is nothing incorrect with his original scenario.

0m/s.

If I define a velocity of 20m/s, I have to define the direction that the object is traveling in. Suppose it's going 20m/s to the east. If I say -20m/s, I am specifying that the object is traveling in the opposite direction -- 20 m/s to the west. That's all it means. When you work with vectors in 2D you usually define one direction as positive and one direction as negative. I imagine it gets more complicated in 3D, but it's still the same basic idea.

They pay Google for every click that draws people to their site. It's how you advertise through Google.

No. Klaynos forgot a qualification: accelerating reference frames are different. All constant-velocity frames are equivalent. You're accelerating because of the way the Earth orbits around the Sun, so your frame is not equivalent with the Sun's.

No. All inertial frames are equivalent and equally valid.

It isn't. But it's been accelerated in a direction opposite to the direction of the train's travel. From the reference frame of the train, it's moving backwards. From that of the rails, it's moving forwards, just more slowly.

As many times as you'd expect for the half-hour trip calculated by D H. Because at high speeds, the person traveling at the high speed experiences length contraction. More info available here and here. As the pilot flies along the measuring tape, he utilizes his ultra-high-speed camera to take a picture of your measuring tape and compare it to his calibrated meterstick on board the spaceship. His meterstick will reveal that the tape has somehow been shrunk -- ten meters suddenly become less than one. You, on the other hand, will think the tape is perfectly normal and his meterstick has shrunk (not grown). Who's right? Both of you. It is counterintuitive, yes. It makes no sense, yes. But it's the way the universe works.

Ran a recount again. I'm unable to experience the problem (it's probably created because of deleted posts in the thread, and I can see those anyway), so is it still happening to you?

This may have something to do with the server's clock being ten minutes off. I'll see if I can get the host to reset the time.