- #1
Vorde
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Homework Statement
The problem is to prove the work-energy theorem: Work is change in kinetic energy.
Homework Equations
Line integral stuff, basic physics stuff.
The Attempt at a Solution
I'm given the normal definitions for acceleration, velocity and I'm given Newton's second law. I'm asked to show that ##\int_c{F \cdot dr}## leads to ##\frac{1}{2}mv(b)^2-\frac{1}{2}mv(a)^2## along an arbitrary path from a to b defined by ##\vec{r}##(t).
I'm stuck. I got to ##Work = m \int_c{ \frac{d \vec{v}}{d \vec{r}} \, \vec{v} \cdot \vec{v} \, dt}##, but I don't know how to proceed with that pesky dot product in the integrand, and without explicit functions to help me simplify, can anyone help?
Thanks a billion.I'll post my work if it seems like I'm going the wrong way, but I don't know where I would be.