Something wrong with the equations of work

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SUMMARY

The discussion centers on the misunderstanding of the work-energy equation, specifically F*d=1/2*mv². The user incorrectly manipulates the equation, leading to a flawed conclusion of 1=1/2. The key error identified is the assumption that velocity (v) remains constant, which is not valid under a constant force scenario. Correctly applying the equations shows that if force is constant, the relationship between distance (d), time (t), and final velocity (v) must be accurately represented as v=2d/t, leading to the correct outcome of 1=1.

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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.
 

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