Physics: I am asking for help to derive a general expression for the total amount of energy lost as a function of time from a radiating object.
I'll simplify my problem like this: Say for example that an object's energy $E$ and velocity $v$ are related by:
$$ E = m v, $$
where $m$ is a constant. The object loses energy at a rate that is proportional to its velocity:
$$ \frac{dE}{dt} = - k v, $$
where $k$ is another constant. Physically, this means that the object's energy will decrease, but will do so at an ever decreasing rate as the velocity decreases along with the falling energy.
If the original ($t=0$) velocity was $v_0$ (or equally, original energy was $E_0$), then can one express the total amount of energy $\Delta E$ radiated (lost) up to an arbitrary time, $t$?
Thanks for any help... this question is similar to that asked here, but I struggled to understand it in terms of my particular problem.