# Mathematical conversion

1. Sep 18, 2014

### namanjain

i was just thinking over line that my teacher told - "Newton's second law is ultimate truth"
i feel why one can say 'F=ma' is more prestigious th 'work energy method' Though i know they are one and same thing, i was planning to derive (using principle of reverse engineering) second law of newton from work energy theorem.
Just help me out tellin' if my method is correct [i donno high-fi vector calculus (not even much of basics)]

W= 1/2mv2
differential form

(dW)=(m)(v)(dv)

F.dx = mvdv
F = mvdv/dx
F = m(dv/dt)

2. Sep 18, 2014

### Staff: Mentor

To some extent that's an aesthetic judgement, so there's no particular reason why you and your teacher have to agree about whether $F=ma$ or $W=fd=(mv^2)/2$ is more fundamental. However, forces and accelerations are things that we can see and feel, whereas work and energy are more mathematical abstractions that we constructed after the fact to help us explain the workings of force and acceleration. Thus, you'll probably find that many people share your teacher's sense of "ultimate truth".

There's nothing wrong with your reverse-engineering exercise - indeed, it pretty much has to come out that way if the theory is consistent (and I presume you and your teacher agree about that).