@layman,
No, Layman. You are wrong.
An object can have a non-zero acceleration at the same time it has a zero velocity... so when you say a non-zero acceleration means an object is "not at rest" you are simply wrong. Let me demonstrate.
The definition of acceleration is given by the function
A(t) = dV/dt
This is the only valid scientific definition of acceleration. So anything you say about acceleration that has any scientific validity has to deal with this function.
So... to demonstrate, let's consider an object that has a velocity at any given time determined by this function
V(t) = 3 - 1.5t
So please (I will let you do the work yourself so you can be sure that you understand).
1) Use the equation for acceleration to calculate the acceleration of this object at time t = 2s (hint: I am sure that after taking the derivative you will see this is a constant acceleration).
2) Evaluate the velocity function at t = 2s.
QED