Something wrong with the equations of work

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The discussion centers on a misunderstanding of the work equation, F*d=1/2*mv², and its application. The original poster attempts to manipulate the equation but arrives at an incorrect conclusion of 1=1/2, questioning if they divided by zero. It is clarified that the assumption of constant velocity (v=d/t) is flawed when a constant force (F) is applied, as this leads to changing velocity. The correct interpretation involves recognizing that with constant force, the relationship between distance and time must account for acceleration, leading to the correct conclusion of 1=1. Understanding these nuances in physics is crucial for accurate calculations.
nhmllr
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Ok, so recently I was introduced work, being
F*d=1/2*mv2
So, naturally I started playing around with it
m*d*v/t = 1/2*m*d/t*d/t
m*d2/t2 = 1/2 * m*d2/t2
1 = 1/2
What did I do wrong here? Did I divide by zero somewhere or something?
(I know that these equations are not relativistically correct but this seems ridiculous)
 
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You assume that v=d/t which isn't correct unless v is constant which is not the case since you assume a (constant) force F is acting which changes v. If we assume F is constant then d=1/2 * v * t or v=2d/t where v here represents the final velocity after distantce d has been traveled. If you replace that v then you finally get 1=1.
 
I have recently been really interested in the derivation of Hamiltons Principle. On my research I found that with the term ##m \cdot \frac{d}{dt} (\frac{dr}{dt} \cdot \delta r) = 0## (1) one may derivate ##\delta \int (T - V) dt = 0## (2). The derivation itself I understood quiet good, but what I don't understand is where the equation (1) came from, because in my research it was just given and not derived from anywhere. Does anybody know where (1) comes from or why from it the...

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