I'm a computer science and math major, but am doing a project
involving escalators (and their engines). In the project, I am making
the assumtion that there is a function (call it E(s)) that gives the
amount of energy that the escalator's engine requires per second to
maintain a given speed "s" (from 0 to 1, where 0 is not moving and 1
is full speed). I am pretty sure that this assumption is valid, but
here's where my question comes in:

I want to know how much energy it takes to change speeds. Say I want to change from s1 to s2. Right now I am thinking that the energy required to do this is the integral of E(s) from s1 to s2. Is this assumption valid? If not, what IS this amount of energy?

Thanks

I want to know how much energy it takes to change speeds. Say I want to change from s1 to s2. Right now I am thinking that the energy required to do this is the integral of E(s) from s1 to s2. Is this assumption valid? If not, what IS this amount of energy?

Thanks