Here's the question you clicked on:
henpen
Power and work \[ W= \int P dt = \int Fv dt= m \int \frac{dv}{dt} vdt=m \int vdv= \frac{1}{2}m(v_1^2-v_0^2) \] Is this true?: -Did I oversimplify somewhere? -Is this unphysical?
\[ W= \int\limits P dt = \int\limits Fv dt= m \int\limits \frac{dv}{dt} vdt=m \int\limits vdv= \frac{1}{2}m(v_1^2-v_0^2) \]
Similarly, \[W=\int\limits_{}^{}Fdx=\int\limits_{}^{}madx=m \int\limits_{}^{} \frac{ dv }{ dt } dx=m \int\limits_{}^{} \frac{ dv }{ dx }\frac{ dx }{ dt } dx = m \int\limits_{}^{} v dv=\frac{ 1 }{ 2 }mv^2\]
@Kainui That's what I did.
No, you did something slightly different. You used power, I did not.