Quote by AdamP
I don't see how you got 1/2 d(v.v)/dt . after that v dot v is v squared magnitude, but how does that help me. dv/dt is a...

If you have an equation with
a (like
F = m
a), you can dot it with
v …
then
v.
a =
v.d
v/dt = 1/2 dv
^{2}/dt, which is easy to integrate.