Hi, this question is about the mathematical justification for a physics topic so hopefully this is the right forum.(adsbygoogle = window.adsbygoogle || []).push({});

All the proofs of the work-KE theorem I have found go something like this:

W= int(F)dx from x1 to x2

= m(int(dv/dt))dx from x1 to x2

= m(int((dv/dt)v)dt from t1 to t2

= (m/2)(vf^2-vi^2) by the chain rule/substitution

My question is regarding the substitution "dx=vdt," and the associated change of variables from x to t, which is obviously true but how do you justify it from the substitution rule or something else not involving differentials? (I'm sure that expression makes perfect sense when it comes to differential forms but I have not learned those yet)

**Physics Forums - The Fusion of Science and Community**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Justification for differential manipulation in work-KE theorem proof

Loading...

Similar Threads - Justification differential manipulation | Date |
---|---|

B Product rule OR Partial differentiation | Jan 10, 2018 |

Justification for cancelling terms in limits? | Aug 13, 2015 |

Justification for evaluation of limits? | Feb 12, 2015 |

Contour integral with a pole on contour - justification? | Nov 22, 2014 |

**Physics Forums - The Fusion of Science and Community**