What is an example of monotonically decelerating/accelerating function? I came across the term monotonically decelerating function. How can it be written as a mathematical function?

Consider the simple case where an object moves along a $1$-dimensional axis.

Usually, the acceleration of an object whose position is represented by $f(t)$ is identified with $f''(t)$. (Recall $f'(t)$ is the speed.) So in this case, $f''(t)$ would have to be a monotonically decreasing function.