If we take F=ma and multiply both sides by dt, we get Fdt = ma dt And then: Fdt = mdv And then: Impulse = change in momentum. OK; I get that. I get a similar process for Work/Energy multiplying F=ma by ds on both sides as follows Fds = ma ds And using a ds = v dv to get Fds = m v dv Work = change in kinetic energy. Now I have been coming to learn that it is not wise to split the derivative For example the form: ads = vdv is possible in 1D. And even then, it is fairly contorted: one should not, in a pure sense, split the derivative. (I have gotten wind of issues like force is a one form and that explains the ds... can we avoid that advanced stuff for now?) Is it possible get to the core of work/energy and impulse/momentum without splitting the derivative?