Why does my derivation give W = mv² instead of KE = 1/2mv²?

[Zula110100100]

I am confused about the KE = 1/2mv²

I was able to get v²=2as from it, by removing mass from each side you get as = 1/2v² then rearrange, but I was trying to relate momentum and work in my head, and since p = mv than KE = 1/2 p * v

but starting with Work = F * s

and since s = vt

Work = F*vt

then solve for time t = W/Fv

and p = mv
v = at
so p = mat

so p = Ft(assuming no original momentum)

substitute for t and

p = FW/Fv

p = W/v

W = pv

W = mv²

So what am I doing wrong? because mv² does not equals 1/2mv²

I was thinking maybe because I am not using t₀ and v₀, but it doesn't seem like that's it, it seems the only way is with the 2as but it should tie back in somewhere...

and even working backwards from KE = 1/2mv²
Fvt = 1/2pv
devide by V and multiply by 2
and p = 2 F*t
p = 2 m*a*t
p = 2 mv

 

[Doc Al]

and since s = vt

Since the speed is not constant, you need to use the average velocity when calculating distance. In the KE formula, the v is the final speed.

 

[Zula110100100]

Oh, okay, so it kinda has to do with not using v_{0[\SUB]...and the like}

 

[Doc Al]

Oh, okay, so it kinda has to do with not using v_{0[\SUB]...and the like}

_{Right. For the simple case of a constant force applied to an object initially at rest (v0 = 0), we'll have vave = v/2. So:
W = F*s = F*v/2*t = (F*t)*v/2 = (mv)*v/2 = 1/2mv². As expected.}