In the algebraic derivation connecting work and kinetic energy for motion along the x-axis

PHYSICS · Subjective · AP · Physics 1: Algebra-based · Work Energy and Power · Work Energy and Power

Problem

In the algebraic derivation connecting work and kinetic energy for motion along the x-axis, why is the product

m\dfrac{dv}{dt}\,v\,dt

used to replace the element of work

F\,dx

? Give a brief reason.