First of all, everyone who took high school physics knows that acceleration can be modeled by the slope of a line gragh, where the x-axis designates time(s), and also where the y-axis designates velocity(m/s).

 

But I have a little paradox that kinda bugs me. Let's say that an object is moving at a constant speed of 5m/s, and then for some reason, (the reason is irrelevant) it just stops without slowing down.

 

Now I plotted it on a graph, and apparently, the acceleration of the object is infinite.

 

Am I missing something here?

No you´re not missing anything. Strictly speaking one could argue whether the acceleration is infinite or simply not defined/existant but that supposedly wasn´t your point. Not all functions have properly defined derivatives and also acceleration does not need to properly exist in physics problems.

 

One classical example where acceleration is not defined is in idealized collisions where the collision takes place at a single time (not over a time period). Within that idalized model, at the point of collision you cannot properly define forces and accelerations. You normally use conservation of momentum and energy plus a geometric assumption to solve the problem, then.