Does acceleration go to zero instantaneously?

[Danieln34]

Here's the scenario: If a force is accelerating an object at a constant rate, and force is removed, does the acceleration instantaneously go to zero? The problem i see with that is that on the graph, the acceleration line would be constant, horizontal, and then when the force is removed to would drop vertically down to zero. Thus, the line is no longer a function. Also the rate of change of the acceleration, or jerk, would not be able to be found since the graph is not differentiable at that point. So is it possible to remove a force instantly? And in a perfect situation, if you could what would the acceleration do? Does anything truly happen instantaneously?

 

[russ_watters]

Mathematically, the answer is yes. You're describing a step function. In reality, objects are not rigid and interact via electromagnetism, so forces don't do step changes.