What is time required for particle, starting from rest, to begin moving under acceleration Without appealing to quantum mech.,what is the time required for a particle, starting from rest, to begin moving under acceleration.
Example: Ball thrown upward comes to rest before descending. How long is it at rest, and how do you calculate the rest time?
 A: Assuming a frictionless environment, if a force is applied to a body, it will start to accelerate immediately. 
The equation $F=m \times a$ can be a little confusing because in reality, the applied force $F$ never goes from $0$ to its final value instantaneously. For example, when I push a table with say $10N$ force, the $10N$ is not applied instantaneously. In reality, as I place my hand on the table and start to push, the force applied slowly increases to its final value.
So if we are told that a force of $10N$ acts on a stationary object of mass $1kg$, the equation $F=m \times a$ would give us an instantaneous acceleration of $10 \frac{m}{s^2}$ but in reality, this $10N$ force would require a finite time to grow (from no force at all [$0N$]) and reach its final value and consequently the acceleration would also increase continuously until it reaches it's final value of $10 \frac{m}{s^2}$
As soon as a body at rest begins to accelerate, it starts moving. The magnitude of displacement depends on the magnitude of the acceleration.  
