Why is the term instantaneous work not defined? I was reading a textbook and found the statement that said that there is no such term as instantaneous work, however the textbook does not give a reason as to why it cannot be defined. To me it sounds perfectly fine to define instantaneous work for particles where force applied remains constant as
$\vec{dF}*\vec{s}$  and if this was not enough many derivations in physics regarding energy do seem to use the term ${dW}$ so what is the problem with instantaneous work?
 A: To do nonzero work you must apply nonzero force across nonzero distance. To speak of something instantaneous you must do it in time $\Delta t \to 0$. To cross nonzero distance in time $\Delta t \to 0$ one needs $v \to \infty$. There is no infinite velocity therefore there is no instantaneous work.

Another way to look at it.
Instantaneous work asks, "How much work is being done right now?" to which the answer is always 0, because right now precludes movement in space and time.
We can still use $dW$ to ask questions about "What happens when an infinitesimal amount of work is done?" Because when any work is done something must have moved through space and time, one answer to that question is always "some time passes".
So not only can we use use $dW$ even though there is no instantaneous work, we actually need $dW$ in order to mathematically define the nonexistence of nonzero instantaneous work:
$$\frac{dt}{dW} \neq 0$$

Since $\frac{dt}{dW}$ is nonzero, the inverse, $\frac{dW}{dt}$ is defined. This is Power, the instantaneous rate of work mentioned by Dale in the comment below.
So, while the answer to "How much work is being done right now?" is always 0, there are many possibilities for the question "Right now, how fast are we doing work?"
A: One may consider an instant work $E(t)$ as a work done up to the current instant $t$ from $t=0$.
