Subjects of Equestria! We are pleased to kick off the Nightmare Night Festivities and the 14th anniversary of the return of our beloved Princess Luna! Join us in celebration!
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Sciencepone of Science!
@mathprofbrony  
To the second equation - multiplying by mass is overrated. I find more often it’s velocity I’m looking for.
 
My guess is she’s just showing it to them, first. Or it’s derived on the left side of the board. I dunno :q
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“The other Twilight was more fun.”  
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“Nothing!”
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She’s just tired. They all are. They’re tired because Twilight’s science lecture is going on for over 6 hours. It’s not necessarily because they’re not interested in physics (Or any science), but because they can’t handle such a long lecture.
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Headcanon: This is part of some court-ordered community service after an entirely innocent misunderstanding that may or may not have involved certain high energy isotopes and a certain horse statue in front of a certain high school. Twilight is following the letter of her punishment rather than the spirit, so that she can get back to doing something important, that those fools could never even begin to understand. They laughed at her at the university. Laughed! But she’ll show them! She’ll show them all!
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In a way, this reminds me of a panel from Marvel’s relaunch of Hulk in the comic form.  
Leucenstern: Don’t you sleep?  
Doc Green/Hulk: No. Not anymore. And especially not when there’s this much science to do.
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Episode where the CMC make a clever project that’s useful for stuff that Applejack insists they enter to the School Science Fair, but Science Twilight finds them and tries to give them advice to “improve” it. They make it into some grand contraption that destroys the fair and a potato lamp wins and a lesson about the importance of letting people learn to solve problems on their own is learned.
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Basic physics of motion. Position (and initial position), velocity (and initial velocity), acceleration, and time.
 
The first and third are essentially the same equation with an error – s and x both mean displacement, or position – and v in the first equation should be v_0. (Psst, Twi: v(t) is ambiguous if you’re multiplying v by t, because it looks like function notation. And if you mean v(t), you’re wrong; just check your units.) It says that your position x is your starting position, x_0, plus the distance you would have traveled at your initial velocity over the interval, v_0 t, plus the distance covered by an object accelerating from a standstill with constant acceleration, 1/2 a t2.
 
The second equation makes more sense if you multiply through by 1/2 m, which then says that kinetic energy (1/2 m v
2) equals initial kinetic energy 1/2 m v_0^2, plus ma(x-x_0). Force is m*a, and force times distance is the work done, which is the change in kinetic energy.
 
Pedagogically, Twi should realize at this point that she’s lost her audience and should either take a break or at least change up the lesson mode, such as turning to some practice.