Why is work=F*d? Derrive without using kinetic energy = square of speed times half of mass

Why is work=F*d? Derrive without using kinetic energy = square of speed times half of mass.

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en.wikipedia.org/wiki/Particle_physics_and_representation_theory
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Isnt work just defined to be dW=Fdr?

for some processes yes.

For a conservative force it is the - gradient of the potential. Literally calc 3

Well, you get that kinetic energy formula from using the definition of work. Work is a definition. Do we need to derive it? Why and from what?

>not understanding potential functions
>not understanding calc 3
>not understanding force as a mapping from R3 to R3

maximum pleb

>forces are all functions of position
>not being a master of quantum electrodyamic fuzzy generalized potentials dependent on the velocity of the observers big toe

It's by definition.
W = int(f dr)
(No latex from phone)
In your specific case, the force is constant along the whole path, and therefor the integral can be simplified.

>(No latex from phone)
No you're just too lazy.
[eqn]W = \int \vec{F} \; dr[/eqn]

That formula is wrong. You have a vector on one side and a scalar on the other.

I'm sure OP is grateful you did his homework for him.

>implying there isnt a hypothetical dot product from the integral

I doubt faggot OP knows what a line integral is.

>21 century
>doing anything in STEM other than generalizing as statistic and linear algebra

this is all there is

A "Dark" dot product, if you will.

>Implying the dr isn't a vector just because it doesn't conform to the same vector notation used by the rest of the formula

So what's your point? That doesn't make the equation any less wrong.

Op here, I don't know integrals and calc.

You will not understand the origin of the equations you encounter in basic physics without calc.

This is why the "algebra-based" physics meme needs to die.

It doesn't help that you have autism.

>"algebra-based" physics meme needs to die
en.wikipedia.org/wiki/Particle_physics_and_representation_theory
Says the undergrad.

[math]W = \int \vec{F} \cdot d\vec{r} [/math]

No there isnt. You have the magnitude of the force times the distance equal the work (scalar)

Kek

You know what I meant.

By definition?

beautiful. Now replace the equality with := and /thread