How Does the Kinetic Energy Formula Work?

[herchi]

Hi i would like to know step by step... how the kinetic formula works.
why we multiply by 1/2, by mass, and by v2...what this means?

 

[bernhard.rothenstein]

Hi i would like to know step by step... how the kinetic formula works.
why we multiply by 1/2, by mass, and by v2...what this means?

Start with the definition of the change in kinetic energy
dW=Fdx=m(dV/dt)V(dt)=mVdV (1)
Integrating (1) with the initial condition V=0; W=0
W=mV²/2
Are all your questions answered?